Ising_Model_Julia.ipynb

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  "metadata": {
    "colab": {
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      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Julia",
      "language": "julia",
      "name": "julia"
    },
    "language_info": {
      "file_extension": ".jl",
      "mimetype": "application/julia",
      "name": "julia"
    },
    "gpuClass": "standard"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Xuanyiyiren/Intersting-things/blob/main/Ising_Model_Julia.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Introduction\n",
        "\n",
        "This is my homework for my course called \"Thermodynamics & Statistical Physics (II)\".\n",
        "\n",
        "My homework refers to a [Rajesh Singh's blog](https://rajeshrinet.github.io/blog/2014/ising-model/). In order to prove that I didn't simply take someone else's program and run it, I reproduced it in the newly learned language `Julia` to complete my homework.\n",
        "\n",
        "My homework has been successfully run on [colab](https://colab.research.google.com/#scrollTo=GJBs_flRovLc), a very convenient platform by Google built for machine learning and AI.\n",
        "\n",
        "This notebook is divided into three parts:\n",
        "1. The first part is preparation for Julia. This part is especially for running Julia on Colab, which only supports Python by default. I also recommend you to run it in this online lab because it might be a bit hard to build Julia's environment on your local device. This way can avoid a lot of strange questions.\n",
        "2. The second part is the main part of my homework, the simulation of the Ising model.\n",
        "3. The third part is a deeper explanation about why I chose Julia and its advantages.\n",
        "\n",
        "To run this notebook, please read the first part carefully and do what it tells you. If you can run the second code block `versioninfo()` well, then you have successfully installed Julia on Colab."
      ],
      "metadata": {
        "id": "oVKPEg4sz4cV"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tQ1r1bbb0yBv"
      },
      "source": [
        "# Preparation for Julia\n",
        "\n",
        "<img src=\"https://github.com/JuliaLang/julia-logo-graphics/raw/master/images/julia-logo-color.png\" height=\"100\" /> _Colab Notebook Template_\n",
        "\n",
        "## Instructions\n",
        "1. Work on a copy of this notebook: _File_ > _Save a copy in Drive_ (you will need a Google account). Alternatively, you can download the notebook using _File_ > _Download .ipynb_, then upload it to [Colab](https://colab.research.google.com/).\n",
        "2. If you need a GPU: _Runtime_ > _Change runtime type_ > _Harware accelerator_ = _GPU_.\n",
        "3. Execute the following cell (click on it and press Ctrl+Enter) to install Julia, IJulia and other packages (if needed, update `JULIA_VERSION` and the other parameters). This takes a couple of minutes.\n",
        "4. Reload this page (press Ctrl+R, or ⌘+R, or the F5 key) and continue to the next section.\n",
        "\n",
        "_Notes_:\n",
        "* If your Colab Runtime gets reset (e.g., due to inactivity), repeat steps 2, 3 and 4.\n",
        "* After installation, if you want to change the Julia version or activate/deactivate the GPU, you will need to reset the Runtime: _Runtime_ > _Factory reset runtime_ and repeat steps 3 and 4."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GIeFXS0F0zww",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        },
        "outputId": "cfee8512-4acc-4ca9-cc36-53ed98ced87a"
      },
      "source": [
        "%%shell\n",
        "set -e\n",
        "\n",
        "#---------------------------------------------------#\n",
        "JULIA_VERSION=\"1.8.2\" # any version ≥ 0.7.0\n",
        "JULIA_PACKAGES=\"IJulia BenchmarkTools\"\n",
        "JULIA_PACKAGES_IF_GPU=\"CUDA\" # or CuArrays for older Julia versions\n",
        "JULIA_NUM_THREADS=2\n",
        "#---------------------------------------------------#\n",
        "\n",
        "if [ -z `which julia` ]; then\n",
        "  # Install Julia\n",
        "  JULIA_VER=`cut -d '.' -f -2 <<< \"$JULIA_VERSION\"`\n",
        "  echo \"Installing Julia $JULIA_VERSION on the current Colab Runtime...\"\n",
        "  BASE_URL=\"https://julialang-s3.julialang.org/bin/linux/x64\"\n",
        "  URL=\"$BASE_URL/$JULIA_VER/julia-$JULIA_VERSION-linux-x86_64.tar.gz\"\n",
        "  wget -nv $URL -O /tmp/julia.tar.gz # -nv means \"not verbose\"\n",
        "  tar -x -f /tmp/julia.tar.gz -C /usr/local --strip-components 1\n",
        "  rm /tmp/julia.tar.gz\n",
        "\n",
        "  # Install Packages\n",
        "  nvidia-smi -L &> /dev/null && export GPU=1 || export GPU=0\n",
        "  if [ $GPU -eq 1 ]; then\n",
        "    JULIA_PACKAGES=\"$JULIA_PACKAGES $JULIA_PACKAGES_IF_GPU\"\n",
        "  fi\n",
        "  for PKG in `echo $JULIA_PACKAGES`; do\n",
        "    echo \"Installing Julia package $PKG...\"\n",
        "    julia -e 'using Pkg; pkg\"add '$PKG'; precompile;\"' &> /dev/null\n",
        "  done\n",
        "\n",
        "  # Install kernel and rename it to \"julia\"\n",
        "  echo \"Installing IJulia kernel...\"\n",
        "  julia -e 'using IJulia; IJulia.installkernel(\"julia\", env=Dict(\n",
        "      \"JULIA_NUM_THREADS\"=>\"'\"$JULIA_NUM_THREADS\"'\"))'\n",
        "  KERNEL_DIR=`julia -e \"using IJulia; print(IJulia.kerneldir())\"`\n",
        "  KERNEL_NAME=`ls -d \"$KERNEL_DIR\"/julia*`\n",
        "  mv -f $KERNEL_NAME \"$KERNEL_DIR\"/julia\n",
        "\n",
        "  echo ''\n",
        "  echo \"Successfully installed `julia -v`!\"\n",
        "  echo \"Please reload this page (press Ctrl+R, ⌘+R, or the F5 key) then\"\n",
        "  echo \"jump to the 'Checking the Installation' section.\"\n",
        "fi"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  Unrecognized magic \u001b[36m%%shell\u001b[39m.\n",
              "\n",
              "  Julia does not use the IPython \u001b[36m%magic\u001b[39m syntax. To interact with the IJulia kernel, use\n",
              "  \u001b[36mIJulia.somefunction(...)\u001b[39m, for example. Julia macros, string macros, and functions can be used to\n",
              "  accomplish most of the other functionalities of IPython magics."
            ],
            "text/markdown": "Unrecognized magic `%%shell`.\n\nJulia does not use the IPython `%magic` syntax.   To interact with the IJulia kernel, use `IJulia.somefunction(...)`, for example.  Julia macros, string macros, and functions can be used to accomplish most of the other functionalities of IPython magics.\n",
            "text/latex": "Unrecognized magic \\texttt{\\%\\%shell}.\n\nJulia does not use the IPython \\texttt{\\%magic} syntax.   To interact with the IJulia kernel, use \\texttt{IJulia.somefunction(...)}, for example.  Julia macros, string macros, and functions can be used to accomplish most of the other functionalities of IPython magics.\n\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-OS3Ac017T1i"
      },
      "source": [
        "## Checking the Installation\n",
        "The `versioninfo()` function should print your Julia version and some other info about the system:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EEzvvzCl1i0F",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a9c7148a-26ad-4c74-ea71-21427e4446f3"
      },
      "source": [
        "versioninfo()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Julia Version 1.8.2\n",
            "Commit 36034abf260 (2022-09-29 15:21 UTC)\n",
            "Platform Info:\n",
            "  OS: Linux (x86_64-linux-gnu)\n",
            "  CPU: 2 × Intel(R) Xeon(R) CPU @ 2.20GHz\n",
            "  WORD_SIZE: 64\n",
            "  LIBM: libopenlibm\n",
            "  LLVM: libLLVM-13.0.1 (ORCJIT, broadwell)\n",
            "  Threads: 2 on 2 virtual cores\n",
            "Environment:\n",
            "  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64\n",
            "  JULIA_NUM_THREADS = 2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Install Packages"
      ],
      "metadata": {
        "id": "fqP6ZyhX2DXb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "using Pkg\n",
        "Pkg.add(\"Plots\")\n",
        "using Plots"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-QJegp7v0LCN",
        "outputId": "a8a54176-f97b-4c80-e9ac-e6b744c8dbd8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.8/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.8/Manifest.toml`\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "gr()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1ce_4k110f-g",
        "outputId": "c35e97e4-9a04-432a-d14d-ac853b6a7f3a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Plots.GRBackend()"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Ising Model"
      ],
      "metadata": {
        "id": "7ka_i5kVzkeV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "function initialstate(N)\n",
        "    2 .* rand(0:1, N, N) .- 1\n",
        "end\n",
        "\n",
        "mymod(n::Int,p::Int) = mod(n-1,p)+1\n",
        "\n",
        "function mcmove(config, beta)\n",
        "    N = size(config)[1]\n",
        "    for i in 1:N^2\n",
        "        a = rand(1:N)\n",
        "        b = rand(1:N)\n",
        "        s = config[a,b]\n",
        "        nb = config[mymod(a+1,N),b] + config[a,mymod(b+1,N)] + config[mymod(a-1,N),b] + config[a,mymod(b-1,N)]\n",
        "        cost = 2*s*nb\n",
        "        if cost<0 || rand(Float64)<exp(-cost*beta)\n",
        "            s*=-1\n",
        "        end\n",
        "        config[a,b] = s\n",
        "    end\n",
        "    return nothing\n",
        "end\n",
        "\n",
        "function calcEnergy(config)\n",
        "    # calculate energy\n",
        "    N = size(config)[1]\n",
        "    energy = 0\n",
        "    for i in 1:N, j in 1:N\n",
        "        s = config[i,j]\n",
        "        nb = config[mymod(i+1,N),j] + config[i,mymod(j+1,N)] + config[mymod(i-1,N),j] + config[i,mymod(j-1,N)]\n",
        "        energy += -nb*s\n",
        "    end\n",
        "    return energy/4\n",
        "end\n",
        "\n",
        "function calcMag(config)\n",
        "    # Magnetization of a given configuration\n",
        "    return sum(config)\n",
        "end"
      ],
      "metadata": {
        "id": "rPSelfuw0iDG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "377a46e7-b3d9-459e-f47e-9dfcd21d788c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "calcMag (generic function with 1 method)"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = initialstate(2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rjaENo0GakP7",
        "outputId": "fcde904b-7c23-4971-95ea-86cfa9c42181"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2×2 Matrix{Int64}:\n",
              "  1  1\n",
              " -1  1"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "nt = 88        # number for temperature sample points\n",
        "N = 16         # size of the lattice\n",
        "eqSteps = 1024 # number of MC sweeps for equilibration\n",
        "mcSteps = 1024 # number of MC sweeps for calculation\n",
        "\n",
        "T_list = range(1.53, 3.28, nt)\n",
        "E,M,C,X = zeros(nt),zeros(nt),zeros(nt),zeros(nt)\n",
        "n1 = 1/(mcSteps*N^2)\n",
        "n2 = n1/mcSteps"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-CDBb2M6PEoD",
        "outputId": "2e42f1cf-b0c7-4a7d-9af4-71b3d515011e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.725290298461914e-9"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for T_index in 1:nt\n",
        "    E1 = M1 = E2 = M2 = 0\n",
        "    config = initialstate(N)\n",
        "    beta = 1/T_list[T_index]\n",
        "    beta2 = beta^2\n",
        "\n",
        "    for i in 1:eqSteps\n",
        "        mcmove(config, beta)\n",
        "    end\n",
        "\n",
        "    for i in 1:mcSteps\n",
        "        mcmove(config,beta)\n",
        "        Ene = calcEnergy(config)\n",
        "        Mag = calcMag(config)\n",
        "\n",
        "        E1 += Ene\n",
        "        M1 += Mag\n",
        "        E2 += Ene^2\n",
        "        M2 += Mag^2\n",
        "    end\n",
        "    E[T_index] = E1*n1\n",
        "    M[T_index] = M1*n1\n",
        "    C[T_index] = (n1*E2 - n2*E1*E1)*beta2\n",
        "    X[T_index] = (n1*M2 - n2*M1*M1)*beta2\n",
        "end"
      ],
      "metadata": {
        "id": "L31dleDpUk_1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p1 = scatter(T_list, E , label = nothing , xlabel = \"Temperature (T)\", ylabel = \"Energy\")\n",
        "p2 = scatter(T_list, M , label = nothing , xlabel = \"Temperature (T)\", ylabel = \"Magnetization\")\n",
        "p3 = scatter(T_list, C , label = nothing , xlabel = \"Temperature (T)\", ylabel = \"Specific Heat\")\n",
        "p4 = scatter(T_list, X , label = nothing , xlabel = \"Temperature (T)\", ylabel = \"Susceptibility\")\n",
        "plot(p1, p2, p3, p4, layout=(2,2),size = (1000,500))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "id": "m86TYlilbrHH",
        "outputId": "6306fbd1-b104-45b4-91bc-1b5b61d0b3df"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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      "source": [
        "The same program takes about $10 \\,\\rm{min}$ in python. But in julia, it only takes $3 \\, \\rm{s}$!\n",
        "\n",
        "This is an amazing result, the Magnetization-Tepmerature plot has tow lines before the critical temperture, one positive and another negtive."
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      "source": [
        "# Why julia\n",
        "\n",
        "## 1. [Julia is a fast](https://github.com/JuliaAcademy/Introduction-to-Julia/blob/main/9%20-%20Julia%20is%20fast.ipynb)\n",
        "\n",
        "Someone has tested the speed of C,python,and julia. He cerate a list with length of $10^7$, and to get the sum of this list. The result is here\n",
        "\n",
        "- C -ffast-math...............1.8\n",
        "- Julia built-in..............1.9\n",
        "- Python numpy................1.9\n",
        "- Julia hand-written simd.....2.4\n",
        "- C...........................9.4\n",
        "- Julia hand-written..........9.4\n",
        "- Python built-in...........875.8\n",
        "- Python hand-written......1011.9\n",
        "\n",
        "We can see that julia is as fast as C! And python is much slower than them.\n",
        "\n",
        "## 2. Julia can run in a interactive nootbook\n",
        "\n",
        "There are tow ways to run julia in notebook:\n",
        "1. [Pluto](https://plutojl.org/): a new types of notebooks with may new feathers.\n",
        "2. [Ijulia](https://julialang.github.io/IJulia.jl/stable/): Like Ipython.\n",
        "\n",
        "Julia can not only runs as fast as C, but also can runs in interactive notebooks! This gives us a big advantages.\n",
        "\n",
        "I originally what to use Pluto, but its package managements confused me. And I only have a limited time to finish this homework.\n",
        "\n",
        "By the way, julia can also be written in a script like C and Matlab.\n",
        "\n",
        "## 3. Julia has many packages especially for scientific computing and many of them are build-in\n",
        "\n",
        "## 4. Julia's grammer is very friendly\n",
        "\n",
        "Julia's grammer is as friendly as Matlab and Mathematica.\n",
        "\n",
        "It is said that julia is the best language for scientific computing."
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}