original_single_flip.ipynb

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   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: replacing module SingleSpinFlip.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Main.SingleSpinFlip"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "module SingleSpinFlip\n",
    "\n",
    "const NDIMS=2\n",
    "using Statistics\n",
    "using Base.Cartesian\n",
    "\n",
    "# Hop to nearest-neighbor site\n",
    "\n",
    "function hop(index::CartesianIndex{NDIMS},dir::Int64,lr::Int64,dims::NTuple{NDIMS,Int64}) where {NDIMS}\n",
    "    # update index\n",
    "    if (lr==1)\n",
    "      hop_index= index[dir]==dims[dir] ? 1 : index[dir]+1\n",
    "    else\n",
    "      hop_index= index[dir]==1 ? dims[dir] : index[dir]-1\n",
    "    end\n",
    "    # generate a new CartesianIndex with updated index\n",
    "    CartesianIndex(Base.setindex(Tuple(index), hop_index, dir))\n",
    "\n",
    "end\n",
    "\n",
    "# Binning + (optionally) bootstrap analysis\n",
    "\n",
    "using Bootstrap\n",
    "function bin_bootstrap_analysis(data;min_sample_size=128,func_boot=nothing,n_boot=1000)\n",
    "    # get total length\n",
    "    data_size=length(data)\n",
    "    # chop to closest power of 2\n",
    "    chopped_data_size=2^floor(Int,log(2,data_size))\n",
    "    chopped_data=collect(Iterators.take(Iterators.reverse(data),chopped_data_size))\n",
    "    # full data std\n",
    "    if func_boot==nothing\n",
    "        stds=[std(chopped_data)/sqrt(chopped_data_size)]\n",
    "    else\n",
    "        # bootstrap\n",
    "        bs = bootstrap(func_boot,chopped_data, BasicSampling(n_boot))\n",
    "        stds=[stderror(bs)[1] ]\n",
    "    end\n",
    "    bin_size=2\n",
    "    while min_sample_size < div(chopped_data_size,bin_size)\n",
    "        # bin size\n",
    "        length_bin=div(chopped_data_size,bin_size)\n",
    "        # binned data\n",
    "        binned=reshape(chopped_data,(bin_size,length_bin))\n",
    "        mean_binned= mean(binned,dims=1)'\n",
    "        # bin std\n",
    "        if func_boot==nothing\n",
    "            std_bin=std(mean_binned)/sqrt(length_bin)\n",
    "        else\n",
    "            # bootstrap\n",
    "            bs = bootstrap(func_boot,mean_binned, BasicSampling(n_boot))\n",
    "            std_bin = stderror(bs)[1]\n",
    "        end\n",
    "        # double bin size\n",
    "        bin_size=bin_size*2\n",
    "        push!(stds,std_bin)\n",
    "    end\n",
    "    stds\n",
    "end\n",
    "\n",
    "# ## MCMC simulation\n",
    "\n",
    "# Simulation parameters\n",
    "mutable struct SimData\n",
    "    # coupling (in units of T)\n",
    "    J::Float64\n",
    "    # size\n",
    "    L::Int64\n",
    "    # numbers of measurements\n",
    "    num_measure::Int64\n",
    "    # numbers of themalization steps\n",
    "    num_thermal::Int64\n",
    "end\n",
    "\n",
    "# Measurements data\n",
    "\n",
    "mutable struct MeasureData\n",
    "    # energy measurement time series\n",
    "    energy::Array{Float64,1}\n",
    "    # magnetization\n",
    "    mag::Array{Float64,1}\n",
    "end\n",
    "function MeasureData(sim_data::SimData)\n",
    "    MeasureData(zeros(sim_data.num_measure),zeros(sim_data.num_measure))\n",
    "end\n",
    "\n",
    "# Simulation data structure\n",
    "\n",
    "mutable struct IsingData\n",
    "    # simulation data\n",
    "    sim_data::SimData\n",
    "    # ising configuration\n",
    "    ising_lat::Array{Int64,NDIMS}\n",
    "    # total energy\n",
    "    total_energy::Int64\n",
    "    # measurements data\n",
    "    measure_data::MeasureData\n",
    "end\n",
    "\n",
    "# Initialization\n",
    "\n",
    "function IsingData(sim_data::SimData)\n",
    "   IsingData(\n",
    "            sim_data,\n",
    "            ones(ntuple(k->sim_data.L,NDIMS )),\n",
    "            NDIMS*sim_data.L^NDIMS,\n",
    "            MeasureData(sim_data)\n",
    "        )\n",
    "end\n",
    "\n",
    "#  Compute single flip $\\Delta E$\n",
    "\n",
    "function calc_delta_E(ising_lat::Array{Int64,NDIMS},pos::CartesianIndex)\n",
    "    delta_E=0\n",
    "    # dims\n",
    "    for d in 1:NDIMS\n",
    "        # left right\n",
    "        for lr in 1:2\n",
    "            # hop to nn\n",
    "            nn=hop(pos,d,lr,size(ising_lat))\n",
    "            # check is the same\n",
    "            if ising_lat[pos]==ising_lat[nn]\n",
    "               delta_E-=2\n",
    "            else\n",
    "               delta_E+=2\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return delta_E\n",
    "end\n",
    "\n",
    "#  Single step\n",
    "\n",
    "function next_step!(ising_data::IsingData)\n",
    "    J=ising_data.sim_data.J\n",
    "    ising_lat=ising_data.ising_lat\n",
    "    # flip site\n",
    "    flip_site=rand(CartesianIndices(ising_lat))\n",
    "    # calculate ratio\n",
    "    delta_E=calc_delta_E(ising_lat,flip_site)\n",
    "    ratio=exp(J*delta_E)\n",
    "    # accept or reject\n",
    "    if ratio>rand()\n",
    "        # flip\n",
    "        ising_lat[flip_site]=-ising_lat[flip_site]\n",
    "        ising_data.total_energy+=delta_E\n",
    "    end\n",
    "end\n",
    "\n",
    "# Make a measurement\n",
    "\n",
    "function make_measurement!(ising_data::IsingData,i)\n",
    "    lat_size=length(ising_data.ising_lat)\n",
    "    # average magnetization\n",
    "    ising_data.measure_data.mag[i]=sum(ising_data.ising_lat)/lat_size\n",
    "    # energy density\n",
    "    ising_data.measure_data.energy[i]=ising_data.total_energy/lat_size\n",
    "end\n",
    "\n",
    "# MCMC run\n",
    "\n",
    "function run_mcmc(sim_data::SimData)\n",
    "    ising_data=IsingData(sim_data)\n",
    "    lat_size=length(ising_data.ising_lat)\n",
    "    # thermalize\n",
    "    for i in 1:sim_data.num_thermal\n",
    "        # sweep\n",
    "        for j in 1:lat_size\n",
    "            next_step!(ising_data)\n",
    "        end\n",
    "    end\n",
    "    # measure\n",
    "    for i in 1:sim_data.num_measure\n",
    "        # sweep\n",
    "        for j in 1:lat_size\n",
    "            next_step!(ising_data)\n",
    "        end\n",
    "        make_measurement!(ising_data,i)\n",
    "    end\n",
    "    ising_data\n",
    "end\n",
    "\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "exact_energy (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function exact_energy(beta,L)\n",
    "    cb=cosh(beta)\n",
    "    sb=sinh(beta)\n",
    "    Z=cb^L+sb^L\n",
    "    (cb^(L-2)+sb^(L-2))*sinh(2*beta)/(2*Z)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "using Statistics\n",
    "using LaTeXStrings\n",
    "gr()\n",
    "betas=range(0.01, length=10,stop=2)\n",
    "Ls=[5,10,20]\n",
    "num_measure=2^16\n",
    "num_thermal=1000\n",
    "fig_en=plot(title=\"energy\")\n",
    "fig_mag=plot(title=\"magnetization\")\n",
    "fig_tau=plot(title=\"correlation time\")\n",
    "for L in Ls\n",
    "    ens=Float64[]\n",
    "    ens_std=Float64[]\n",
    "    mags=Float64[]\n",
    "    mags_std=Float64[]\n",
    "    taus=Float64[]\n",
    "    for b in betas\n",
    "        sim_data=SingleSpinFlip.SimData(b,L,num_measure,num_thermal)\n",
    "        res=SingleSpinFlip.run_mcmc(sim_data)\n",
    "        push!(ens,mean(res.measure_data.energy))\n",
    "        stds=SingleSpinFlip.bin_bootstrap_analysis(res.measure_data.energy)\n",
    "        push!(ens_std,stds[end])\n",
    "        push!(mags,mean(res.measure_data.mag))\n",
    "        stds=SingleSpinFlip.bin_bootstrap_analysis(res.measure_data.mag)\n",
    "        push!(mags_std,stds[end])\n",
    "        tau=0.5*((stds[end]/stds[1])^2-1)\n",
    "        push!(taus,tau)\n",
    "    end\n",
    "    plot!(fig_en,betas,ens,yerr =ens_std,xlabel=L\"\\beta\",ylabel=L\"E\",label=\"mc L=$L\",legend=:bottomright)\n",
    "#     plot!(fig_en,betas,[exact_energy(b,L) for b in betas],label=\"exact L=$L\",legend=:bottomright)\n",
    "    plot!(fig_mag,betas,mags,yerr =mags_std,xlabel=L\"\\beta\",ylabel=L\"m\",label=\"L=$L\",legend=:topleft)\n",
    "    plot!(fig_tau,betas,taus,label=\"L=$L\",xlabel=L\"\\beta\",ylabel=L\"\\tau\",legend=:topleft)\n",
    "end\n",
    "fig=plot(fig_en,fig_mag,fig_tau,layout=grid(1,3),size = (1200, 600))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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