MC.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"./perov_functions.jl\")\n",
    "using Plots\n",
    "using BenchmarkTools\n",
    "using Distributions\n",
    "using LaTeXStrings\n",
    "using Measures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=2;nk=100;\n",
    "system_original=make_symstem(n);\n",
    "system=copy(system_original);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.0, -0.0, -0.0]\n",
      "[-0.0, -0.0, 0.0]\n",
      "[-0.0, 0.0, 0.0]\n",
      "[-0.0, 0.0, 0.0]\n",
      "[-0.0, -0.0, 0.0]\n",
      "[-0.0, -0.0, 0.0]\n",
      "[-0.0, 0.0, 0.0]\n",
      "[-0.0, 0.0, 0.0]\n"
     ]
    }
   ],
   "source": [
    "s1=make_symstem(n);\n",
    "s2=make_system_wo(n);\n",
    "for i in 1:length(s1)\n",
    "    println(round.(s1[i].cl2-s2[i].cl2,digits=3))\n",
    "    end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function e1(system)\n",
    "    axis=rand(Uniform(-1.,1.),3)\n",
    "    theta=rand(Uniform(0,2π))\n",
    "    pos=rand(1:size(system)[1],3)\n",
    "    s,s1=get_rotation_energy_1(system,1,1/250,pos,axis,theta);\n",
    "    if s<0\n",
    "        system=s1\n",
    "        end;\n",
    "    e=get_total_energy_mag(system,1,1/150)\n",
    "    return e\n",
    "    end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "function run_sum(n,system,g1,g2)\n",
    "    e=[]\n",
    "    a1=[]\n",
    "    a2=[]\n",
    "    a3=[]\n",
    "    mag_val=[]\n",
    "    for i in 1:n\n",
    "        axis=rand(Uniform(-1.,1.),3)\n",
    "        theta=rand(Uniform(0,2π))\n",
    "        pos=rand(1:size(system)[1],3)\n",
    "        s,s1=get_rotation_energy_1(system,g1,g2,pos,axis,theta);\n",
    "        if s<0\n",
    "            system=s1\n",
    "            end;\n",
    "        if i%100==0\n",
    "            vals=get_total_energy_mag(system,g1,g2)\n",
    "            energy=vals[1]\n",
    "            angles=vals[2].^2\n",
    "            push!(e,energy)\n",
    "            push!(a1,angles[1])\n",
    "            push!(a2,angles[2])\n",
    "            push!(a3,angles[3])\n",
    "            push!(mag_val,norm(vals[2]))\n",
    "            end;\n",
    "        end;\n",
    "    return e,a1,a2,a3,mag_val,system\n",
    "    end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 29.081049 seconds (309.01 M allocations: 34.007 GiB, 25.15% gc time)\n"
     ]
    }
   ],
   "source": [
    "system=copy(system_original);\n",
    "@time e,a1,a2,a3,mag_val,system=run_sum(60000,system,1,1/950);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "function animplots(i)\n",
    "gr()\n",
    "pl1=plot((1:i)*100,e[1:i],ylabel=\"energy\",xlabel=\"iterations\",color=RGB(226/255, 194/255, 144/255),label=\"\",linewidth=2)\n",
    "pl2=plot((1:i)*100,a1[1:i],label=L\"$s_x$\",xlabel=\"iterations\",ylabel=\"component\",ylim=(-0.01,1.1),linewidth=1.5)\n",
    "plot!(pl2,(1:i)*100,a2[1:i],label=L\"$s_y$\",linewidth=1.5)\n",
    "plot!(pl2,(1:i)*100,a3[1:i],label=L\"$s_z$\",linewidth=1.5)\n",
    "pl3=plot((1:i)*100,mag_val[1:i],ylabel=L\"$M$\",xlabel=\"iterations\",color=RGB(202/255, 255/255, 191/255),linewidth=2,label=\"\",ylim=(-0.01,1.1))\n",
    "hline!(pl3,[1],linestyle=:dash,color=\"grey\",label=\"\")\n",
    "hline!(pl2,[1/3],linestyle=:dash,color=\"grey\",label=\"\")\n",
    "plot(pl1,pl3,pl2,size=(1200,400),dpi=100,bottom_margin=5mm,layout=@layout [a b c])\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "anim = @animate for i ∈ 1:length(e)\n",
    "    animplots(i)\n",
    "end\n",
    "gif(anim, \"animations/MC_3.gif\", fps = 17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19"
     ]
    }
   ],
   "source": [
    "cnt=0\n",
    "for i in 1:100\n",
    "    axis=rand(Uniform(-1.,1.),3)\n",
    "    theta=rand(Uniform(0,2π))\n",
    "    pos=rand(1:size(system)[1],3)\n",
    "    dE,s1=get_rotation_energy_1(system,1,1/250,pos,axis,theta);\n",
    "    T=.2\n",
    "    if dE < 0 || rand() < exp(-dE/T)\n",
    "        cnt+=1\n",
    "    end\n",
    "end\n",
    "print(cnt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot of Monoclinic !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plotly()\n",
    "pl=plot()\n",
    "system=copy(system_original);\n",
    "axis=[0,1,0.]\n",
    "system[1,2,1]=rot_tetra_test_1(system[1,2,1],axis,pi)\n",
    "system[2,1,1]=rot_tetra_test_1(system[2,1,1],axis,pi)\n",
    "system[1,2,2]=rot_tetra_test_1(system[1,2,2],axis,pi)\n",
    "system[2,1,2]=rot_tetra_test_1(system[2,1,2],axis,pi)\n",
    "coords=[[0,0,1],[0,1,0],[1,0,0]]*15\n",
    "for i in coords\n",
    "    plot!(pl,[0,i[1]],[0,i[2]],[0,i[3]],linewidth=5,color=\"red\",linestyle=:dash,label=\"\")\n",
    "    end;\n",
    "t=get_total_energy_mag(system,0,1)[2]*10\n",
    "plot!(pl,[0,t[1]],[0,t[2]],[0,t[3]],linewidth=2,color=\"yellow\",label=\"\")\n",
    "for i in system\n",
    "    plot_tetra(i,pl)\n",
    "    t=get_dipol_vec(i)\n",
    "    plot!(pl,[0,t[1]],[0,t[2]],[0,t[3]],linewidth=5,color=\"white\",label=\"\")\n",
    "    end;\n",
    "display(pl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get coupling constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "function get_g(de)\n",
    "    n=2\n",
    "    system_original=make_symstem(n);\n",
    "    system=copy(system_original);\n",
    "    axis=[0,1,0.]\n",
    "    system[1,2,1]=rot_tetra_test_1(system[1,2,1],axis,pi)\n",
    "    system[2,1,1]=rot_tetra_test_1(system[2,1,1],axis,pi)\n",
    "    system[1,2,2]=rot_tetra_test_1(system[1,2,2],axis,pi)\n",
    "    system[2,1,2]=rot_tetra_test_1(system[2,1,2],axis,pi)\n",
    "    u_m=get_total_energy_mag(system,0,1)[1]\n",
    "    d_m=get_total_energy_mag(system,1,0)[1]\n",
    "    u_p=get_total_energy_mag(system_original,0,1)[1]\n",
    "    d_p=get_total_energy_mag(system_original,1,0)[1];\n",
    "    return (de-(d_p-d_m))/(u_p-u_m)\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g=0.0032311983843898487  Check δE(0.095)=0.09500000000000008\n"
     ]
    }
   ],
   "source": [
    "g=get_g(-0.095)\n",
    "Ep =g*get_total_energy_mag(system,0,1)[1]+get_total_energy_mag(system,1,0)[1]\n",
    "Em=g*get_total_energy_mag(system_original,0,1)[1]+get_total_energy_mag(system_original,1,0)[1];\n",
    "println(\"g=$g  Check δE(0.095)=$(Ep-Em)\") #= =0.095? =#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MC with new g value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "function run_sum(n,system,g1,g2)\n",
    "    e=[]\n",
    "    a1=[]\n",
    "    a2=[]\n",
    "    a3=[]\n",
    "    mag_val=[]\n",
    "    for i in 1:n\n",
    "        axis=rand(Uniform(-1.,1.),3)\n",
    "        theta=rand(Uniform(0,2π))\n",
    "        pos=rand(1:size(system)[1],3)\n",
    "        s,s1=get_rotation_energy_1(system,g1,g2,pos,axis,theta);\n",
    "        if s<0\n",
    "            system=s1\n",
    "            end;\n",
    "        if i%100==0\n",
    "            vals=get_total_energy_mag(system,g1,g2)\n",
    "            energy=vals[1]\n",
    "            angles=vals[2].^2\n",
    "            push!(e,energy)\n",
    "            push!(a1,angles[1])\n",
    "            push!(a2,angles[2])\n",
    "            push!(a3,angles[3])\n",
    "            push!(mag_val,norm(vals[2]))\n",
    "            end;\n",
    "        end;\n",
    "    return e,a1,a2,a3,mag_val,system\n",
    "    end;\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "g=get_g(-0.095)\n",
    "n=5;nk=100;\n",
    "system=make_symstem(n);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 31.919422 seconds (349.36 M allocations: 38.381 GiB, 21.63% gc time)\n"
     ]
    }
   ],
   "source": [
    "@time e,a1,a2,a3,mag_val,system=run_sum(000,system,0,1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
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       "  1873.62,1240.05 1875.7,1282.99 1877.77,1304.22 1879.84,1286.23 1881.91,1282.79 1883.98,1293.58 1886.05,1297.05 1888.13,1330.42 1890.2,1330.25 1892.27,1344.72 \n",
       "  1894.34,1332.83 1896.41,1325.14 1898.48,1335.66 1900.56,1334.35 1902.63,1348.39 1904.7,1349.76 1906.77,1352.87 1908.84,1360.2 1910.91,1355.93 1912.99,1361.84 \n",
       "  1915.06,1351.36 1917.13,1339.19 1919.2,1341.19 1921.27,1342.45 1923.34,1342.98 1925.42,1357.93 1927.49,1355.5 1929.56,1357.52 1931.63,1357.57 1933.7,1359.04 \n",
       "  1935.77,1366.59 1937.85,1366.45 1939.92,1369.73 1941.99,1366.57 1944.06,1370.1 1946.13,1365.71 1948.2,1373.61 1950.28,1370.33 1952.35,1372.36 1954.42,1372.15 \n",
       "  1956.49,1369.99 1958.56,1359.69 1960.63,1364.86 1962.71,1362.88 1964.78,1366.26 1966.85,1364.68 1968.92,1370.73 1970.99,1368.65 1973.06,1372.76 1975.14,1369.88 \n",
       "  1977.21,1371.36 1979.28,1373.91 1981.35,1374.57 1983.42,1369.53 1985.49,1369.73 1987.57,1374.46 1989.64,1370.52 1991.71,1370.98 1993.78,1370.19 1995.85,1370.09 \n",
       "  1997.92,1371.32 2000,1375.58 2002.07,1372.55 2004.14,1370.43 2006.21,1372.22 2008.28,1372.65 2010.35,1373.23 2012.43,1374.82 2014.5,1376.19 2016.57,1375.99 \n",
       "  2018.64,1378.59 2020.71,1377.69 2022.78,1377.33 2024.86,1374.09 2026.93,1377.79 2029,1377.08 2031.07,1375.32 2033.14,1371.44 2035.21,1368.94 2037.29,1372.78 \n",
       "  2039.36,1377.31 2041.43,1378.32 2043.5,1376.99 2045.57,1378.48 2047.64,1376.84 2049.71,1379.73 2051.79,1374.29 2053.86,1375.35 2055.93,1382.73 2058,1380.5 \n",
       "  2060.07,1382.63 2062.14,1384.01 2064.22,1383.71 2066.29,1384.05 2068.36,1383.99 2070.43,1381.02 2072.5,1380.97 2074.57,1380.97 2076.65,1380.13 2078.72,1383.92 \n",
       "  2080.79,1381.03 2082.86,1381.12 2084.93,1380.94 2087,1380.1 2089.08,1380.11 2091.15,1379.27 2093.22,1380.21 2095.29,1381.78 2097.36,1381.9 2099.43,1381.53 \n",
       "  2101.51,1381.53 2103.58,1380.46 2105.65,1380.64 2107.72,1380.76 2109.79,1381.39 2111.86,1381.78 2113.94,1380.4 2116.01,1379.13 2118.08,1379.63 2120.15,1380.12 \n",
       "  2122.22,1380.4 2124.29,1380.11 2126.37,1378.66 2128.44,1377.59 2130.51,1377.4 2132.58,1376 2134.65,1376.54 2136.72,1380.87 2138.8,1381.72 2140.87,1381.52 \n",
       "  2142.94,1380.87 2145.01,1380.91 2147.08,1381.02 2149.15,1381.77 2151.23,1381.77 2153.3,1381.93 2155.37,1382.4 2157.44,1382.4 2159.51,1383.74 2161.58,1383.76 \n",
       "  2163.66,1384.07 2165.73,1384.9 2167.8,1384.51 2169.87,1385.67 2171.94,1386.27 2174.01,1386.19 2176.09,1386.26 2178.16,1384.35 2180.23,1385.1 2182.3,1385.1 \n",
       "  2184.37,1384.91 2186.44,1384.91 2188.52,1384.05 2190.59,1384.07 2192.66,1384.09 2194.73,1382.59 2196.8,1382.69 2198.87,1382.94 2200.95,1382.94 2203.02,1383.07 \n",
       "  2205.09,1383.4 2207.16,1383.62 2209.23,1383.48 2211.3,1383.23 2213.38,1383.48 2215.45,1383.96 2217.52,1384.21 2219.59,1384.22 2221.66,1383.83 2223.73,1383.87 \n",
       "  2225.81,1383.87 2227.88,1383.95 2229.95,1383.93 2232.02,1383.84 2234.09,1383.84 2236.16,1383.52 2238.23,1383.79 2240.31,1383.45 2242.38,1383.45 2244.45,1384.27 \n",
       "  2246.52,1384.1 2248.59,1383.69 2250.66,1383.92 2252.74,1384.12 2254.81,1384.12 2256.88,1383.04 2258.95,1383.6 2261.02,1383.6 2263.09,1384.58 2265.17,1384.57 \n",
       "  2267.24,1384.56 2269.31,1384.56 2271.38,1383.03 2273.45,1383.1 2275.52,1382.43 2277.6,1382.53 2279.67,1382.91 2281.74,1382.91 2283.81,1383.31 2285.88,1383.22 \n",
       "  2287.95,1383.29 2290.03,1384.46 2292.1,1384.78 2294.17,1384.59 2296.24,1383.99 2298.31,1384.07 2300.38,1385.19 2302.46,1384.99 2304.53,1383.87 2306.6,1384.01 \n",
       "  2308.67,1383.98 2310.74,1383.66 2312.81,1383.66 2314.89,1382.59 2316.96,1383.42 2319.03,1383.74 2321.1,1383.74 2323.17,1384.99 2325.24,1385.42 2327.32,1386.31 \n",
       "  2329.39,1386.66 2331.46,1386.8 2333.53,1386.8 2335.6,1386.67 2337.67,1387.24 2339.75,1387.24 2341.82,1387.6 2343.89,1387.6 2345.96,1386.5 2348.03,1386.72 \n",
       "  2350.1,1386.72 2352.18,1386.7 2354.25,1386.7 2356.32,1386.81 2358.39,1385.23 2360.46,1385.06 2362.53,1384.91 2364.61,1384.63 2366.68,1384.44 2368.75,1384.48 \n",
       "  2370.82,1384.48 2372.89,1385.06 2374.96,1383.65 2377.04,1383.65 2379.11,1383.32 2381.18,1383.13 2383.25,1383.13 2385.32,1383.13 2387.39,1385.07 2389.47,1384.91 \n",
       "  2391.54,1384.91 2393.61,1384.97 2395.68,1384.69 2397.75,1384.82 2399.82,1384.75 2401.9,1384.81 2403.97,1385.16 2406.04,1385.16 2408.11,1385.29 2410.18,1384.9 \n",
       "  2412.25,1384.9 2414.32,1384.9 2416.4,1384.45 2418.47,1384.45 2420.54,1385.03 2422.61,1385.03 2424.68,1385.03 2426.75,1385.03 2428.83,1385.34 2430.9,1385.61 \n",
       "  2432.97,1385.61 2435.04,1386.11 2437.11,1386.57 2439.18,1386.57 2441.26,1386.68 2443.33,1386.68 2445.4,1386.7 2447.47,1387.65 2449.54,1387.52 2451.61,1386.57 \n",
       "  2453.69,1386.8 2455.76,1385.93 2457.83,1385.79 2459.9,1386.21 2461.97,1386.38 2464.04,1386.38 2466.12,1385.6 2468.19,1385.24 2470.26,1385.3 2472.33,1385.3 \n",
       "  2474.4,1384.93 2476.47,1385.17 2478.55,1385.17 2480.62,1385.17 2482.69,1384.8 2484.76,1384.8 2486.83,1384.01 2488.9,1384.01 2490.98,1384.01 2493.05,1384.01 \n",
       "  2495.12,1384.01 2497.19,1384.12 2499.26,1384.11 2501.33,1384.23 2503.41,1383.82 2505.48,1384.02 2507.55,1384.01 2509.62,1383.93 2511.69,1383.74 2513.76,1384.1 \n",
       "  2515.84,1384.64 2517.91,1384.75 2519.98,1384.68 2522.05,1384.49 2524.12,1384.49 2526.19,1384.33 2528.27,1384.34 2530.34,1383.69 2532.41,1382.83 2534.48,1382.75 \n",
       "  2536.55,1382.85 2538.62,1382.87 2540.7,1383.1 2542.77,1382.66 2544.84,1382.63 2546.91,1382.6 2548.98,1382.6 2551.05,1382.6 2553.13,1382.59 2555.2,1382.59 \n",
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      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function animplots(i)\n",
    "gr()\n",
    "pl1=plot((1:i)*100,e[1:i],ylabel=\"energy\",xlabel=\"iterations\",color=RGB(226/255, 194/255, 144/255),label=\"\",linewidth=2)\n",
    "pl2=plot((1:i)*100,a1[1:i],label=L\"$s_x$\",xlabel=\"iterations\",ylabel=\"component\",ylim=(-0.01,1.1),linewidth=1.5)\n",
    "plot!(pl2,(1:i)*100,a2[1:i],label=L\"$s_y$\",linewidth=1.5)\n",
    "plot!(pl2,(1:i)*100,a3[1:i],label=L\"$s_z$\",linewidth=1.5)\n",
    "pl3=plot((1:i)*100,mag_val[1:i],ylabel=L\"$M$\",xlabel=\"iterations\",color=RGB(202/255, 255/255, 191/255),linewidth=2,label=\"\",ylim=(-0.01,1.1))\n",
    "hline!(pl3,[1],linestyle=:dash,color=\"grey\",label=\"\")\n",
    "hline!(pl2,[1/3],linestyle=:dash,color=\"grey\",label=\"\")\n",
    "plot(pl1,pl3,pl2,size=(1200,400),dpi=100,bottom_margin=5mm,layout=@layout [a b c])\n",
    "end;\n",
    "animplots(length(e))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Int64,Any} with 1 entry:\n",
       "  104 => Dict{Int64,Any}(#= circular reference @-1 =#)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty!(Out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.4.1",
   "language": "julia",
   "name": "julia-1.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}