Schroeder_Section_3p3_Paramagnetism.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "194250d0",
   "metadata": {},
   "source": [
    "# Generating tables and figures in Schroeder 3.3 Paramagnetism\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70df13c9",
   "metadata": {},
   "source": [
    "We have a two-state paramagnet with $N$ dipoles. The number of dipoles pointing up is $N_\\uparrow$.\n",
    "\n",
    "The total number of states is $2^N$ and the multiplicity of $N_\\uparrow$ (i.e., the number of microstates in this macrostate) is\n",
    "$$\n",
    " \\Omega(N,N_\\uparrow) = \\frac{N!}{N_\\uparrow! (N-N_\\uparrow)!} = \\frac{N!}{N_\\uparrow! (N-N_\\uparrow)!} = {N\\choose N_\\uparrow} \\,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4030f05a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from scipy.special import comb\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "42321cda",
   "metadata": {},
   "outputs": [],
   "source": [
    "def para_energy_over_muB(N, Nup):\n",
    "    \"\"\"\n",
    "    Calculate the energy of a 2-state paramagnet\n",
    "    \"\"\"\n",
    "    return N - 2 * Nup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "47c6f68c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def para_magnetization_over_mu(N, Nup):\n",
    "    \"\"\"\n",
    "    Calculate the magnetization of a 2-state paramagnet\n",
    "    \"\"\"\n",
    "    Ndown = N - Nup\n",
    "    return (Nup - Ndown) / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ca5adc15",
   "metadata": {},
   "outputs": [],
   "source": [
    "def para_mult(N, Nup):\n",
    "    \"\"\"\n",
    "    Calculate the 2-state paramagnet multiplicity and return it as\n",
    "     an integer.\n",
    "    \"\"\"\n",
    "    return int(comb(N, Nup))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a138491f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def para_entropy_over_k(N, Nup):\n",
    "    \"\"\"\n",
    "    Calculate the 2-state paramagnet entropy divided by k (so just the\n",
    "      ln of the multiplicity).\n",
    "    \"\"\"\n",
    "    return np.log(np.float64(para_mult(N,Nup)))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f787e765",
   "metadata": {},
   "outputs": [],
   "source": [
    "def convert_int(my_int, large=10**6):\n",
    "    \"\"\"\n",
    "    If my_int is larger than large, return an exponential form.\n",
    "      The right justification for ints should be log10(large) + 1.\n",
    "    \"\"\"\n",
    "    if my_int > large:\n",
    "        return \"{: .1e}\".format(my_int)\n",
    "    else:\n",
    "        return \"{:>8}\".format(my_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fb44b344",
   "metadata": {},
   "outputs": [],
   "source": [
    "def round_to_n(num, sigfigs):\n",
    "    \"\"\"\n",
    "    Round off num to the specifie number of sigfigs (significant figures)\n",
    "    \"\"\"\n",
    "    if num == 0:\n",
    "        return num\n",
    "    else:\n",
    "        return round(num, -int(math.floor(math.log10(abs(num)))) + (sigfigs - 1))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9659ab47",
   "metadata": {},
   "outputs": [],
   "source": [
    "def central_diff(array1, array2, index):\n",
    "    \"\"\"\n",
    "    Calculate the derivative of array at index by central difference\n",
    "    \"\"\"\n",
    "    return (array1[index + 1] - array1[index - 1]) / \\\n",
    "           (array2[index + 1] - array2[index - 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a1613450",
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_diff(array1, array2, index):\n",
    "    \"\"\"\n",
    "    Calculate the derivative of array at index by forward difference\n",
    "    \"\"\"\n",
    "    return (array1[index + 1] - array1[index]) / \\\n",
    "           (array2[index + 1] - array2[index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "317a3fe4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_diff(array1, array2, index):\n",
    "    \"\"\"\n",
    "    Calculate the derivative of array at index by central difference\n",
    "    \"\"\"\n",
    "    return (array1[index] - array1[index - 1]) / \\\n",
    "           (array2[index] - array2[index - 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "02329029",
   "metadata": {},
   "outputs": [],
   "source": [
    "def second_deriv(array, index):\n",
    "    \"\"\"\n",
    "    Calculate the 2nd derivative of an array at index \n",
    "    \"\"\"\n",
    "    return ( array[index + 1] - 2 * array[index]  \\\n",
    "             + array[index - 1] )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9ca77faf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def properties_table(N, table=True):\n",
    "    \"\"\"\n",
    "    Step through Nup from 0 to N and use para_mult to find \n",
    "      the multiplicity Omega. \n",
    "   \n",
    "    Construct a table like in Schroeder 3.2.\n",
    "      \n",
    "    If table=False, don't print the table but return the arrays.\n",
    "    \"\"\"\n",
    "    if table:\n",
    "        print(' Nup U/muB  M/Nmu     Omega   S/k    kT/muB   C/Nk ')\n",
    "\n",
    "    # Collect values in arrays\n",
    "    Nup_array = np.zeros(N+1, dtype=int) \n",
    "    U_over_muB_array = np.zeros(N+1, dtype=int)\n",
    "    M_over_mu_array = np.zeros(N+1)\n",
    "    Omega_array = np.zeros(N+1)  \n",
    "    S_over_k_array = np.zeros(N+1)\n",
    "    kT_over_muB_array = np.zeros(N+1)\n",
    "    C_over_Nk_array = np.zeros(N+1)\n",
    "    C_over_Nk_array2 = np.zeros(N+1)\n",
    "    \n",
    "    for Nup in range(N+1):\n",
    "        Nup_array[Nup] = int(Nup)\n",
    "        U_over_muB_array[Nup] = int(para_energy_over_muB(N, Nup))\n",
    "        M_over_mu_array[Nup] = para_magnetization_over_mu(N, Nup)\n",
    "        Omega_array[Nup] = para_mult(N, Nup) \n",
    "        S_over_k_array[Nup] = para_entropy_over_k(N, Nup) \n",
    "        \n",
    "    # Find the temperature by central or forward/backward differences\n",
    "    for Nup in range(N+1):\n",
    "        if Nup > 0 and Nup < N:\n",
    "            T = 1 / central_diff(S_over_k_array, U_over_muB_array, Nup) \n",
    "        elif Nup == 0:\n",
    "            T = 1 / forward_diff(S_over_k_array, U_over_muB_array, Nup)\n",
    "        elif Nup == N:\n",
    "            T = 1 / backward_diff(S_over_k_array, U_over_muB_array, Nup)\n",
    "        if T == np.inf or T == -np.inf:\n",
    "            True\n",
    "            #T = 0\n",
    "        else:\n",
    "            #T = T\n",
    "            T = round_to_n(T, 2)\n",
    "        kT_over_muB_array[Nup] = T\n",
    "\n",
    "    # Find C_over_Nk by central or forward/backward differences\n",
    "    #  Two different methods tried\n",
    "    for Nup in range(N+1):\n",
    "        if Nup > 0 and Nup < N:\n",
    "            CB = central_diff(U_over_muB_array, kT_over_muB_array, Nup) \n",
    "            CB2 = -4 / second_deriv(S_over_k_array, Nup) \\\n",
    "                        / kT_over_muB_array[Nup]**2\n",
    "        elif Nup == 0:\n",
    "            CB = 0\n",
    "            CB2 = 0\n",
    "        elif Nup == N:\n",
    "            CB = 0\n",
    "            CB2 = 0\n",
    "        C_over_Nk_array[Nup] = CB / N\n",
    "        C_over_Nk_array2[Nup] = CB2 / N\n",
    "        \n",
    "    if table:\n",
    "        for Ndown in range(N+1):\n",
    "            Nup = N - Ndown\n",
    "            print (f'{Nup_array[Nup]:> 4} ',\n",
    "                   f'{U_over_muB_array[Nup]:> 4} ',\n",
    "                   f'{M_over_mu_array[Nup]: .2f} ',\n",
    "                   f'{convert_int(Omega_array[Nup])}',\n",
    "                   f' {S_over_k_array[Nup]:5.2f} ',\n",
    "                   f' {kT_over_muB_array[Nup]: 4.2f} ', \\\n",
    "                   f' {C_over_Nk_array[Nup]: 4.3f} ' \\\n",
    "                  )\n",
    "\n",
    "    return Nup_array, U_over_muB_array, M_over_mu_array, \\\n",
    "               Omega_array, S_over_k_array, kT_over_muB_array, \\\n",
    "               C_over_Nk_array, C_over_Nk_array2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fce35aa1",
   "metadata": {},
   "source": [
    "## Table 3.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ec57aa44",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Nup U/muB  M/Nmu     Omega   S/k    kT/muB   C/Nk \n",
      " 100  -100   1.00       1.0   0.00    0.43    0.000 \n",
      "  99   -98   0.98     100.0   4.61    0.47    0.364 \n",
      "  98   -96   0.96    4950.0   8.51    0.54    0.308 \n",
      "  97   -94   0.94  161700.0  11.99    0.60    0.364 \n",
      "  96   -92   0.92   3.9e+06  15.18    0.65    0.400 \n",
      "  95   -90   0.90   7.5e+07  18.14    0.70    0.400 \n",
      "  94   -88   0.88   1.2e+09  20.90    0.75    0.444 \n",
      "  93   -86   0.86   1.6e+10  23.50    0.79    0.444 \n",
      "  92   -84   0.84   1.9e+11  25.95    0.84    0.444 \n",
      "  91   -82   0.82   1.9e+12  28.27    0.88    0.444 \n",
      "  90   -80   0.80   1.7e+13  30.48    0.93    0.444 \n",
      "  89   -78   0.78   1.4e+14  32.58    0.97    0.571 \n",
      "  88   -76   0.76   1.1e+15  34.59    1.00    0.308 \n",
      "  87   -74   0.74   7.1e+15  36.50    1.10    0.400 \n",
      "  86   -72   0.72   4.4e+16  38.33    1.10    0.400 \n",
      "  85   -70   0.70   2.5e+17  40.07    1.20    0.400 \n",
      "  84   -68   0.68   1.3e+18  41.74    1.20    0.400 \n",
      "  83   -66   0.66   6.7e+18  43.34    1.30    0.400 \n",
      "  82   -64   0.64   3.1e+19  44.87    1.30    0.400 \n",
      "  81   -62   0.62   1.3e+20  46.33    1.40    0.200 \n",
      "  80   -60   0.60   5.4e+20  47.73    1.50    0.400 \n",
      "  79   -58   0.58   2.0e+21  49.07    1.50    0.400 \n",
      "  78   -56   0.56   7.3e+21  50.35    1.60    0.200 \n",
      "  77   -54   0.54   2.5e+22  51.57    1.70    0.200 \n",
      "  76   -52   0.52   8.0e+22  52.73    1.80    0.400 \n",
      "  75   -50   0.50   2.4e+23  53.85    1.80    0.400 \n",
      "  74   -48   0.48   7.0e+23  54.90    1.90    0.200 \n",
      "  73   -46   0.46   1.9e+24  55.91    2.00    0.200 \n",
      "  72   -44   0.44   5.0e+24  56.87    2.10    0.133 \n",
      "  71   -42   0.42   1.2e+25  57.78    2.30    0.133 \n",
      "  70   -40   0.40   2.9e+25  58.64    2.40    0.200 \n",
      "  69   -38   0.38   6.6e+25  59.46    2.50    0.133 \n",
      "  68   -36   0.36   1.4e+26  60.22    2.70    0.100 \n",
      "  67   -34   0.34   2.9e+26  60.95    2.90    0.133 \n",
      "  66   -32   0.32   5.8e+26  61.63    3.00    0.100 \n",
      "  65   -30   0.30   1.1e+27  62.26    3.30    0.080 \n",
      "  64   -28   0.28   2.0e+27  62.85    3.50    0.080 \n",
      "  63   -26   0.26   3.4e+27  63.40    3.80    0.067 \n",
      "  62   -24   0.24   5.7e+27  63.90    4.10    0.057 \n",
      "  61   -22   0.22   9.0e+27  64.37    4.50    0.044 \n",
      "  60   -20   0.20   1.4e+28  64.79    5.00    0.036 \n",
      "  59   -18   0.18   2.0e+28  65.17    5.60    0.031 \n",
      "  58   -16   0.16   2.8e+28  65.51    6.30    0.025 \n",
      "  57   -14   0.14   3.8e+28  65.81    7.20    0.019 \n",
      "  56   -12   0.12   4.9e+28  66.07    8.40    0.014 \n",
      "  55   -10   0.10   6.1e+28  66.29    10.00    0.009 \n",
      "  54    -8   0.08   7.3e+28  66.47    13.00    0.006 \n",
      "  53    -6   0.06   8.4e+28  66.61    17.00    0.003 \n",
      "  52    -4   0.04   9.3e+28  66.70    25.00    0.001 \n",
      "  51    -2   0.02   9.9e+28  66.76    50.00   -0.000 \n",
      "  50     0   0.00   1.0e+29  66.78   -inf   -0.000 \n",
      "  49     2  -0.02   9.9e+28  66.76   -50.00    0.000 \n",
      "  48     4  -0.04   9.3e+28  66.70   -25.00    0.001 \n",
      "  47     6  -0.06   8.4e+28  66.61   -17.00    0.003 \n",
      "  46     8  -0.08   7.3e+28  66.47   -13.00    0.006 \n",
      "  45    10  -0.10   6.1e+28  66.29   -10.00    0.009 \n",
      "  44    12  -0.12   4.9e+28  66.07   -8.40    0.014 \n",
      "  43    14  -0.14   3.8e+28  65.81   -7.20    0.019 \n",
      "  42    16  -0.16   2.8e+28  65.51   -6.30    0.025 \n",
      "  41    18  -0.18   2.0e+28  65.17   -5.60    0.031 \n",
      "  40    20  -0.20   1.4e+28  64.79   -5.00    0.036 \n",
      "  39    22  -0.22   9.0e+27  64.37   -4.50    0.044 \n",
      "  38    24  -0.24   5.7e+27  63.90   -4.10    0.057 \n",
      "  37    26  -0.26   3.4e+27  63.40   -3.80    0.067 \n",
      "  36    28  -0.28   2.0e+27  62.85   -3.50    0.080 \n",
      "  35    30  -0.30   1.1e+27  62.26   -3.30    0.080 \n",
      "  34    32  -0.32   5.8e+26  61.63   -3.00    0.100 \n",
      "  33    34  -0.34   2.9e+26  60.95   -2.90    0.133 \n",
      "  32    36  -0.36   1.4e+26  60.22   -2.70    0.100 \n",
      "  31    38  -0.38   6.6e+25  59.46   -2.50    0.133 \n",
      "  30    40  -0.40   2.9e+25  58.64   -2.40    0.200 \n",
      "  29    42  -0.42   1.2e+25  57.78   -2.30    0.133 \n",
      "  28    44  -0.44   5.0e+24  56.87   -2.10    0.133 \n",
      "  27    46  -0.46   1.9e+24  55.91   -2.00    0.200 \n",
      "  26    48  -0.48   7.0e+23  54.90   -1.90    0.200 \n",
      "  25    50  -0.50   2.4e+23  53.85   -1.80    0.400 \n",
      "  24    52  -0.52   8.0e+22  52.73   -1.80    0.400 \n",
      "  23    54  -0.54   2.5e+22  51.57   -1.70    0.200 \n",
      "  22    56  -0.56   7.3e+21  50.35   -1.60    0.200 \n",
      "  21    58  -0.58   2.0e+21  49.07   -1.50    0.400 \n",
      "  20    60  -0.60   5.4e+20  47.73   -1.50    0.400 \n",
      "  19    62  -0.62   1.3e+20  46.33   -1.40    0.200 \n",
      "  18    64  -0.64   3.1e+19  44.87   -1.30    0.400 \n",
      "  17    66  -0.66   6.7e+18  43.34   -1.30    0.400 \n",
      "  16    68  -0.68   1.3e+18  41.74   -1.20    0.400 \n",
      "  15    70  -0.70   2.5e+17  40.07   -1.20    0.400 \n",
      "  14    72  -0.72   4.4e+16  38.33   -1.10    0.400 \n",
      "  13    74  -0.74   7.1e+15  36.50   -1.10    0.400 \n",
      "  12    76  -0.76   1.1e+15  34.59   -1.00    0.308 \n",
      "  11    78  -0.78   1.4e+14  32.58   -0.97    0.571 \n",
      "  10    80  -0.80   1.7e+13  30.48   -0.93    0.444 \n",
      "   9    82  -0.82   1.9e+12  28.27   -0.88    0.444 \n",
      "   8    84  -0.84   1.9e+11  25.95   -0.84    0.444 \n",
      "   7    86  -0.86   1.6e+10  23.50   -0.79    0.444 \n",
      "   6    88  -0.88   1.2e+09  20.90   -0.75    0.444 \n",
      "   5    90  -0.90   7.5e+07  18.14   -0.70    0.400 \n",
      "   4    92  -0.92   3.9e+06  15.18   -0.65    0.400 \n",
      "   3    94  -0.94  161700.0  11.99   -0.60    0.364 \n",
      "   2    96  -0.96    4950.0   8.51   -0.54    0.308 \n",
      "   1    98  -0.98     100.0   4.61   -0.47    0.364 \n",
      "   0   100  -1.00       1.0   0.00   -0.43    0.000 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/1s/3wbqg65x5k79l5ww8fg25yvh0000gn/T/ipykernel_87242/1281449247.py:33: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  T = 1 / central_diff(S_over_k_array, U_over_muB_array, Nup)\n"
     ]
    }
   ],
   "source": [
    "N_para = 100\n",
    "Nup_array, U_over_muB_array, M_over_mu_array, \\\n",
    "Omega_array, S_over_k_array, kT_over_muB_array, \\\n",
    "C_over_Nk_array, C_over_Nk_array2 = properties_table(N_para)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb52b794",
   "metadata": {},
   "source": [
    "## Figures 3.8, 3.9, and 3.10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77c10803",
   "metadata": {},
   "source": [
    "We'll add analytic solutions to the numerical ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "61275e7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def kT_over_muB_exact(U_over_muB, N):\n",
    "    \"\"\"\n",
    "    Use equation 3.30\n",
    "    \"\"\"\n",
    "    return 2 / np.log( (N - U_over_muB) / (N + U_over_muB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a5ea6f1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def M_over_muN_exact(kT_over_muB):\n",
    "    \"\"\"\n",
    "    Use equation 3.32\n",
    "    \"\"\"\n",
    "    return np.tanh(1 / kT_over_muB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2e1c9722",
   "metadata": {},
   "outputs": [],
   "source": [
    "def CB_over_Nk_exact(kT_over_muB):\n",
    "    \"\"\"\n",
    "    Use equation 3.32\n",
    "    \"\"\"\n",
    "    return (1 / kT_over_muB)**2 / np.cosh(1 / kT_over_muB)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "765d878e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/1s/3wbqg65x5k79l5ww8fg25yvh0000gn/T/ipykernel_87242/3294786009.py:5: RuntimeWarning: divide by zero encountered in divide\n",
      "  return 2 / np.log( (N - U_over_muB) / (N + U_over_muB))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 2)\n",
    "\n",
    "axs[0,0].plot(U_over_muB_array, S_over_k_array, color='blue')\n",
    "axs[0,0].set_xlabel(r'$U/\\mu B$')\n",
    "axs[0,0].set_ylabel(r'$S/k$')\n",
    "axs[0,0].set_xlim(U_over_muB_array[-1], U_over_muB_array[0])\n",
    "axs[0,0].text(0.5, 0.2, 'Figure 3.8', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[0,0].transAxes)\n",
    "\n",
    "U_over_muBN_exact1 = np.arange(-1, 0, .01)\n",
    "kT_over_muB_exact_array1 = kT_over_muB_exact(N_para*U_over_muBN_exact1, N_para)\n",
    "U_over_muBN_exact2 = np.arange(0, 1, .01)\n",
    "kT_over_muB_exact_array2 = kT_over_muB_exact(N_para*U_over_muBN_exact2, N_para)\n",
    "axs[0,1].plot(U_over_muB_array/N_para, kT_over_muB_array, color='blue')\n",
    "axs[0,1].plot(U_over_muBN_exact1, kT_over_muB_exact_array1, color='red', ls=':', lw=3)\n",
    "axs[0,1].plot(U_over_muBN_exact2, kT_over_muB_exact_array2, color='red', ls=':', lw=3)\n",
    "axs[0,1].set_xlabel(r'$U/N \\mu B$')\n",
    "axs[0,1].set_ylabel(r'$kT / \\mu B$')\n",
    "axs[0,1].set_xlim(-1, 1)\n",
    "axs[0,1].set_ylim(-20, 20)\n",
    "axs[0,1].text(0.75, 0.8, 'Figure 3.9', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[0,1].transAxes)\n",
    "\n",
    "kT_over_muB_CB_array = np.arange(0.01, 8, .01)\n",
    "CB_over_Nk_exact_array = CB_over_Nk_exact(kT_over_muB_CB_array)\n",
    "axs[1,0].plot(kT_over_muB_array, C_over_Nk_array, color='blue')\n",
    "axs[1,0].plot(kT_over_muB_CB_array, CB_over_Nk_exact_array, color='red', ls=':', lw=3)\n",
    "axs[1,0].set_xlabel(r'$kT / \\mu B$')\n",
    "axs[1,0].set_ylabel(r'$C/N k$')\n",
    "axs[1,0].set_xlim(0, 7.2)\n",
    "axs[1,0].set_ylim(0, 0.5)\n",
    "axs[1,0].text(0.75, 0.8, 'Figure 3.10a', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[1,0].transAxes)\n",
    "\n",
    "kT_over_muB_M_array1 = np.arange(-12, 0, .01)\n",
    "M_over_muN_exact_array1 = M_over_muN_exact(kT_over_muB_M_array1)\n",
    "kT_over_muB_M_array2 = np.arange(0, 12, .01)\n",
    "M_over_muN_exact_array2 = M_over_muN_exact(kT_over_muB_M_array2)\n",
    "axs[1,1].plot(kT_over_muB_array, M_over_mu_array, color='blue')\n",
    "axs[1,1].plot(kT_over_muB_M_array1, M_over_muN_exact_array1, color='red', ls=':', lw=3)\n",
    "axs[1,1].plot(kT_over_muB_M_array2, M_over_muN_exact_array2, color='red', ls=':', lw=3)\n",
    "axs[1,1].set_xlabel(r'$kT / \\mu B$')\n",
    "axs[1,1].set_ylabel(r'$M/N \\mu$')\n",
    "axs[1,1].set_xlim(-10, 10)\n",
    "axs[1,1].set_ylim(-1, 1)\n",
    "axs[1,1].text(0.25, 0.8, 'Figure 3.10a', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[1,1].transAxes)\n",
    "\n",
    "\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0604e283",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/1s/3wbqg65x5k79l5ww8fg25yvh0000gn/T/ipykernel_87242/3294786009.py:5: RuntimeWarning: divide by zero encountered in divide\n",
      "  return 2 / np.log( (N - U_over_muB) / (N + U_over_muB))\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 2)\n",
    "\n",
    "axs[0,0].plot(U_over_muB_array, S_over_k_array, color='blue')\n",
    "axs[0,0].set_xlabel(r'$U/\\mu B$')\n",
    "axs[0,0].set_ylabel(r'$S/k$')\n",
    "axs[0,0].set_xlim(U_over_muB_array[-1], U_over_muB_array[0])\n",
    "axs[0,0].text(0.5, 0.2, 'Figure 3.8', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[0,0].transAxes)\n",
    "\n",
    "U_over_muBN_exact1 = np.arange(-1, 0, .01)\n",
    "kT_over_muB_exact_array1 = kT_over_muB_exact(N_para*U_over_muBN_exact1, N_para)\n",
    "U_over_muBN_exact2 = np.arange(0, 1, .01)\n",
    "kT_over_muB_exact_array2 = kT_over_muB_exact(N_para*U_over_muBN_exact2, N_para)\n",
    "axs[0,1].plot(U_over_muB_array/N_para, kT_over_muB_array, color='blue')\n",
    "axs[0,1].plot(U_over_muBN_exact1, kT_over_muB_exact_array1, color='red', ls=':', lw=3)\n",
    "axs[0,1].plot(U_over_muBN_exact2, kT_over_muB_exact_array2, color='red', ls=':', lw=3)\n",
    "axs[0,1].set_xlabel(r'$U/N \\mu B$')\n",
    "axs[0,1].set_ylabel(r'$kT / \\mu B$')\n",
    "axs[0,1].set_xlim(-1, 1)\n",
    "axs[0,1].set_ylim(-20, 20)\n",
    "axs[0,1].text(0.75, 0.8, 'Figure 3.9', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[0,1].transAxes)\n",
    "\n",
    "kT_over_muB_CB_array = np.arange(0.01, 8, .01)\n",
    "CB_over_Nk_exact_array = CB_over_Nk_exact(kT_over_muB_CB_array)\n",
    "axs[1,0].plot(kT_over_muB_array, C_over_Nk_array2, color='blue')\n",
    "axs[1,0].plot(kT_over_muB_CB_array, CB_over_Nk_exact_array, color='red', ls=':', lw=3)\n",
    "axs[1,0].set_xlabel(r'$kT / \\mu B$')\n",
    "axs[1,0].set_ylabel(r'$C/N k$')\n",
    "axs[1,0].set_xlim(0, 7.2)\n",
    "axs[1,0].set_ylim(0, 0.5)\n",
    "axs[1,0].text(0.75, 0.8, 'Figure 3.10a', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[1,0].transAxes)\n",
    "\n",
    "kT_over_muB_M_array1 = np.arange(-12, 0, .01)\n",
    "M_over_muN_exact_array1 = M_over_muN_exact(kT_over_muB_M_array1)\n",
    "kT_over_muB_M_array2 = np.arange(0, 12, .01)\n",
    "M_over_muN_exact_array2 = M_over_muN_exact(kT_over_muB_M_array2)\n",
    "axs[1,1].plot(kT_over_muB_array, M_over_mu_array, color='blue')\n",
    "axs[1,1].plot(kT_over_muB_M_array1, M_over_muN_exact_array1, color='red', ls=':', lw=3)\n",
    "axs[1,1].plot(kT_over_muB_M_array2, M_over_muN_exact_array2, color='red', ls=':', lw=3)\n",
    "axs[1,1].set_xlabel(r'$kT / \\mu B$')\n",
    "axs[1,1].set_ylabel(r'$M/N \\mu$')\n",
    "axs[1,1].set_xlim(-10, 10)\n",
    "axs[1,1].set_ylim(-1, 1)\n",
    "axs[1,1].text(0.25, 0.8, 'Figure 3.10a', horizontalalignment='center',\n",
    "     verticalalignment='center', transform=axs[1,1].transAxes)\n",
    "\n",
    "\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "593293e8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "727d81c5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}