Spin sampling

[cossio]

Here are two ways of sampling spins.

using LogExpFunctions, Random

function _sample_1(θ)
    u = rand(eltype(θ), size(θ))
    return ifelse.(u .* (1 .+ exp.(-2θ)) .≤ 1, Int8(1), Int8(-1))
end

function _sample_2(θ)
    u = randexp(eltype(θ), size(θ))
    return ifelse.(2θ .≥ u .- log1mexp.(u), Int8(1), Int8(-1))
end

and their benchmarks

So implement the first.