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#!/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::Float64
magnetization::Int
mc_steps::Int
accepted_moves::Int
energy_array::Vector{Float64}
magnetization_array::Vector{Int}
H::Float64
end
Ising2D(l::Int, temperature::Float64, H = 1.0) = 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 = Float64(-2 * n + 2 * H * n)
magnetization = n
return Ising2D(l, n, temperature, w, state, energy, magnetization, 0, 0,
Int[], Int[], H)
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
changed_spins = 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)])
de = 2 * changed_spins + 2 * ising.H * state[i, j]
if de <= 0 || rand() < exp(-de / ising.temperature)
accepted_moves += 1
new_spin = -state[i, j] # flip spin
state[i, j] = new_spin
# add the effects of the 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
function find_m(H::Float64, l::Int, num::Int, T::Float64)
m = Ising2D(l, T, H)
steps!(m, num)
print("T = $T\n")
print("H = $H\n")
print("Mean Energy: $(mean_energy(m))\n")
print("Mean Magnetization: $(mean_magnetization(m))\n\n")
return mean_magnetization(m)
end
function map_h_to_m(H_range::Vector{Float64}, l::Int, num::Int, T::Float64)
m = []
for H in H_range
push!(m, find_m(H, l, num, T))
end
return m
end
function do_linear_regression(x::Vector{Float64}, y::Vector{Float64})
n = length(x)
x̄ = mean(x)
ȳ = mean(y)
Σxy = sum((x .- x̄) .* (y .- ȳ))
Σx² = sum((x .- x̄) .^ 2)
b = Σxy / Σx²
a = ȳ - b * x̄
return a, b
end
function plot_log_of_m_and_h(H_range::Vector{Float64}, l::Int, num::Int, T = 2.27)
m = map_h_to_m(H_range, l, num, T)
p = scatter(H_range, m, label = "M vs H", xlabel = "H", ylabel = "M", title = "Magnetization (M) vs Field (B) for Ising Model at T_c", scale = :ln)
# get the linear regression of the log
log_h = log.(H_range)
log_m = log.(m)
a, b = do_linear_regression(log_h, log_m)
println("a: $a, b: $b")
# plot the linear regression
plot!(p, H_range, exp.(a) .* H_range .^ b, label = "linear regression = $(round(a, digits=3)) + $(round(b, digits=3))x", line = :dash, color = :red)
savefig(p, "hw7/magnetization_vs_field.png")
return p
end
# textbook rec
h_range = 0.02:0.02:0.2
h_range = collect(h_range)
T = 2.27 # T_c for this system
side = 64
steps = 5000
plot_log_of_m_and_h(h_range, side, steps)
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