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Diffstat (limited to 'hw6/IsingModel.jl')
-rw-r--r-- | hw6/IsingModel.jl | 141 |
1 files changed, 141 insertions, 0 deletions
diff --git a/hw6/IsingModel.jl b/hw6/IsingModel.jl new file mode 100644 index 0000000..d1e04de --- /dev/null +++ b/hw6/IsingModel.jl @@ -0,0 +1,141 @@ +#!/Applications/Julia-1.7.app/Contents/Resources/julia/bin/julia + +using Statistics +using Plots + +function wrap_index(i::Int, l::Int)::Int + wrap = (i - 1) % l + 1 + return (wrap <= 0) ? l + wrap : wrap +end + +mutable struct Ising2D + l::Int + n::Int + temperature::Float64 + w::Vector{Float64} # Boltzmann weights + state::Matrix + energy::Int + magnetization::Int + mc_steps::Int + accepted_moves::Int + energy_array::Vector{Int} + magnetization_array::Vector{Int} +end + +Ising2D(l::Int, temperature::Float64) = begin + n = l^2 + w = zeros(9) + w[9] = exp(-8.0 / temperature) + w[5] = exp(-4.0 / temperature) + state = ones(Int, l, l) # initially all spins up + energy = -2 * n + magnetization = n + return Ising2D(l, n, temperature, w, state, energy, magnetization, 0, 0, + Int[], Int[]) +end + +function reset!(ising::Ising2D) + ising.mc_steps = 0 + ising.accepted_moves = 0 + ising.energy_array = Int[] + ising.magnetization_array = Int[] +end + +function mc_step!(ising::Ising2D) + l::Int = ising.l + n::Int = ising.n + w = ising.w + + state = ising.state + accepted_moves = ising.accepted_moves + energy = ising.energy + magnetization = ising.magnetization + + random_positions = l * rand(2 * n) + random_array = rand(n) + + for k in 1:n + i = trunc(Int, random_positions[2 * k - 1]) + 1 + j = trunc(Int, random_positions[2 * k]) + 1 + + de = 2 * state[i, j] * (state[i % l + 1, j] + + state[wrap_index(i - 1, l), j] + state[i, j % l + 1] + + state[i, wrap_index(j - 1, l)]) + + if de <= 0 || w[de + 1] > random_array[k] + accepted_moves += 1 + new_spin = - state[i, j] # flip spin + state[i, j] = new_spin + energy += de + magnetization += 2 * new_spin + end + + end + + ising.state = state + ising.accepted_moves = accepted_moves + ising.energy = energy + ising.magnetization = magnetization + + append!(ising.energy_array, ising.energy) + append!(ising.magnetization_array, ising.magnetization) + ising.mc_steps = ising.mc_steps + 1 +end + +function steps!(ising::Ising2D, num::Int=100) + for i in 1:num + mc_step!(ising) + end +end + +function mean_energy(ising::Ising2D) + return mean(ising.energy_array) / ising.n +end + +function specific_heat(ising::Ising2D) + return (std(ising.energy_array) / ising.temperature) ^ 2 / ising.n +end + +function mean_magnetization(ising::Ising2D) + return mean(ising.magnetization_array) / ising.n +end + +function susceptibility(ising::Ising2D) + return (std(ising.magnetization_array)) ^ 2 / (ising.temperature * ising.n) +end + +function observables(ising::Ising2D) + printstyled("Temperature\t\t", bold=true) + print(ising.temperature); print("\n") + + printstyled("Mean Energy\t\t", bold=true) + print(mean_energy(ising)); print("\n") + + printstyled("Mean Magnetiz.\t\t", bold=true) + print(mean_magnetization(ising)); print("\n") + + printstyled("Specific Heat\t\t", bold=true) + print(specific_heat(ising)); print("\n") + + printstyled("Susceptibility\t\t", bold=true) + print(susceptibility(ising)); print("\n") + + printstyled("MC Steps\t\t", bold=true) + print(ising.mc_steps); print("\n") + printstyled("Accepted Moves\t\t", bold=true) + print(ising.accepted_moves); print("\n") +end + + +function plot_ising(state::Matrix{Int}) + pos = Tuple.(findall(>(0), state)) + neg = Tuple.(findall(<(0), state)) + scatter(pos, markersize=5) + scatter!(neg, markersize=5) +end + + +m = Ising2D(32, 2.3) +steps!(m, 1000) +observables(m) +plot_ising(m.state) |