testing

1 files changed, 191 insertions, 0 deletions

diff --git a/hw7/8-12.jl b/hw7/8-12.jl
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+++ b/hw7/8-12.jl
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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)
+
+    return p
+end
+
+# textbook rec
+h_range = .02:.02:.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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