{
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   "cell_type": "markdown",
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   "source": [
    "## Heat Bath Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random, math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 6\n",
    "N = L * L\n",
    "nbr = {i : ((i // L) * L + (i + 1) % L, (i + L) % N,\n",
    "            (i // L) * L + (i - 1) % L, (i - L) % N) for i in range(N)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsteps = 1000\n",
    "beta = 1.0\n",
    "S = [random.choice([-1, 1]) for site in range(N)]\n",
    "\n",
    "E = -0.5 * sum(S[k] * sum(S[nn] for nn in nbr[k]) \\\n",
    "                               for k in range(N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_tot, E2_tot = 0.0, 0.0\n",
    "random.seed('123456')\n",
    "for step in range(nsteps):\n",
    "    k = random.randint(0, N - 1)\n",
    "    Upsilon = random.uniform(0.0, 1.0)\n",
    "    h = sum(S[nn] for nn in nbr[k])\n",
    "    Sk_old = S[k]\n",
    "    S[k] = -1\n",
    "    if Upsilon < 1.0 / (1.0 + math.exp(-2.0 * beta * h)):\n",
    "        S[k] = 1\n",
    "    if S[k] != Sk_old:\n",
    "        E -= 2.0 * h * S[k]\n",
    "    E_tot += E\n",
    "    E2_tot += E ** 2\n",
    "E_av  = E_tot / float(nsteps)\n",
    "E2_av = E2_tot / float(nsteps)\n",
    "c_V = beta ** 2 * (E2_av - E_av ** 2) / float(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-55.988, 7.750662666666661)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_av,c_V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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   "execution_count": null,
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   "source": []
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   "execution_count": null,
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   "execution_count": null,
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   "source": []
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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  {
   "cell_type": "code",
   "execution_count": null,
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