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HB.jl
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#classical J1-J2 Heisenberg model
#Heatbath method
#Annealing
abstract type ModelParameters end
struct mp <: ModelParameters
L::Int64
J1::Float64 # neareast neighbor exchange coupling
J2::Float64 # next-neareast neighbor exchange coupling
runs::Int64
Tmin::Float64
Tmax::Float64
Tsteps::Int64
deltaT::Float64
mcs_max::Int64 #Maximum number of MC steps
discard::Int64 #Thermalization
frac::Int64
inext::Array{Int64,1}
iprev::Array{Int64,1}
function mp(L::Int64, J1::Float64, J2::Float64, runs::Int64, Tmin::Float64, Tmax::Float64, Tsteps::Int64, mcs_max::Int64, discard::Int64)
deltaT = (Tmax - Tmin) / (Tsteps - 1)
inext, iprev = neighbor_indices(L)
frac = mcs_max - discard
new(L, J1, J2, runs, Tmin, Tmax, Tsteps, deltaT, mcs_max, discard, frac, inext, iprev)
end
end
sintheta(c) = sqrt(1 - clamp(c, -1.0, 1.0)^2)
SiSj(pi, pj, ci, cj) = cos(pi - pj) * sintheta(ci) * sintheta(cj) + ci * cj
function neighbor_indices(L::Integer)
inext = [i < L ? i + 1 : 1 for i in 1:L]
iprev = [i > 1 ? i - 1 : L for i in 1:L]
return inext, iprev
end
function compute_hlocal(phi, costheta, ix, iy, inextx, inexty, iprevx, iprevy, J1, J2)
hlocalx = 0.0
hlocaly = 0.0
hlocalz = 0.0
J1isnotzero = !iszero(J1)
J2isnotzero = !iszero(J2)
if J1isnotzero
sinthetapx = sintheta(costheta[inextx, iy])
sinthetamx = sintheta(costheta[iprevx, iy])
sinthetapy = sintheta(costheta[ix, inexty])
sinthetamy = sintheta(costheta[ix, iprevy])
hlocalx += J1 * (cos(phi[inextx, iy]) * sinthetapx + cos(phi[iprevx, iy]) * sinthetamx
+ cos(phi[ix, inexty]) * sinthetapy + cos(phi[ix, iprevy]) * sinthetamy)
hlocaly += J1 * (sin(phi[inextx, iy]) * sinthetapx + sin(phi[iprevx, iy]) * sinthetamx
+ sin(phi[ix, inexty]) * sinthetapy + sin(phi[ix, iprevy]) * sinthetamy)
hlocalz += J1 * (costheta[inextx, iy] + costheta[iprevx, iy] + costheta[ix, inexty] + costheta[ix, iprevy])
end
if J2isnotzero
sinthetapxpy = sintheta(costheta[inextx, inexty])
sinthetapxmy = sintheta(costheta[inextx, iprevy])
sinthetamxpy = sintheta(costheta[iprevx, inexty])
sinthetamxmy = sintheta(costheta[iprevx, iprevy])
hlocalx += J2 * (cos(phi[inextx, inexty]) * sinthetapxpy + cos(phi[inextx, iprevy]) * sinthetapxmy
+ cos(phi[iprevx, inexty]) * sinthetamxpy + cos(phi[iprevx, iprevy]) * sinthetamxmy)
hlocaly += J2 * (sin(phi[inextx, inexty]) * sinthetapxpy + sin(phi[inextx, iprevy]) * sinthetapxmy
+ sin(phi[iprevx, inexty]) * sinthetamxpy + sin(phi[iprevx, iprevy]) * sinthetamxmy)
hlocalz += J2 * (costheta[inextx, inexty] + costheta[inextx, iprevy] + costheta[iprevx, inexty] + costheta[iprevx, iprevy])
end
return hlocalx, hlocaly, hlocalz
end
function observe_ene(mp::ModelParameters, phi, costheta)
tmpE = 0.0
inext = mp.inext
iprev = mp.iprev
L = mp.L
J1 = mp.J1
J2 = mp.J2
J1isnotzero = !iszero(J1)
J2isnotzero = !iszero(J2)
for ix in 1:L, iy in 1:L
phixy = phi[ix, iy]
costhetaxy = costheta[ix, iy]
ixnext = inext[ix]
iynext = inext[iy]
ixprev = iprev[ix]
iyprev = iprev[iy]
if J1isnotzero
tmpE += J1 * (
SiSj(phixy, phi[ix, iynext], costhetaxy, costheta[ix, iynext])
+ SiSj(phixy, phi[ix, iyprev], costhetaxy, costheta[ix, iyprev])
+ SiSj(phixy, phi[ixnext, iy], costhetaxy, costheta[ixnext, iy])
+ SiSj(phixy, phi[ixprev, iy], costhetaxy, costheta[ixprev, iy])
)
end
if J2isnotzero
tmpE += J2 * (
SiSj(phixy, phi[ixnext, iynext], costhetaxy, costheta[ixnext, iynext])
+ SiSj(phixy, phi[ixnext, iyprev], costhetaxy, costheta[ixnext, iyprev])
+ SiSj(phixy, phi[ixprev, iynext], costhetaxy, costheta[ixprev, iynext])
+ SiSj(phixy, phi[ixprev, iyprev], costhetaxy, costheta[ixprev, iyprev])
)
end
end
return tmpE
end
function update_HB!(mp::ModelParameters, phi, costheta, T)
L = mp.L
inext = mp.inext
iprev = mp.iprev
for ix in 1:L, iy in 1:L
hlocalx, hlocaly, hlocalz = compute_hlocal(phi, costheta, ix, iy, inext[ix], inext[iy], iprev[ix], iprev[iy], mp.J1, mp.J2)
hlocalxy = hlocalx^2 + hlocaly^2
sqrt_hlocalxy = sqrt(hlocalxy)
sqrt_hlocalxyz = sqrt(hlocalxy + hlocalz^2)
betaH = sqrt_hlocalxyz / T
sznew = -1 - log1p(rand() * expm1(-2 * betaH)) / betaH
sinthetanew = sintheta(sznew)
cpsi = hlocalz / sqrt_hlocalxyz
spsi = sintheta(cpsi)
cphi = hlocalx / sqrt_hlocalxy
sphi = hlocaly / sqrt_hlocalxy
phi_rand = 2pi * rand()
sxnew = cos(phi_rand) * sinthetanew
synew = sin(phi_rand) * sinthetanew
sx = cpsi * cphi * sxnew - sphi * synew + spsi * cphi * sznew
sy = cpsi * sphi * sxnew + cphi * synew + spsi * sphi * sznew
costheta[ix, iy] = -spsi * sxnew + cpsi * sznew
# mod is necessary to transform the angle from [-pi,pi] to [0,2pi]
phi[ix, iy] = mod(atan(sy, sx), 2pi)
end
end
function main(mp::ModelParameters)
Tsteps = mp.Tsteps
L = mp.L
runs = mp.runs
deltaT = mp.deltaT
frac = mp.frac
discard = mp.discard
ave_ene = zeros(Tsteps)
var_ene = zeros(Tsteps)
ave_spec = zeros(Tsteps)
var_spec = zeros(Tsteps)
Ts = [mp.Tmax - deltaT * (Tstep - 1) for Tstep in 1:Tsteps]
for run in 1:runs
phi = 2pi * rand(L, L)
costheta = 2rand(L, L) .- 1
#phi=zeros(L,L);costheta=zeros(L,L)
for Tstep in 1:Tsteps
energy = 0.0
energy2 = 0.0
T = Ts[Tstep]
for mcs in 1:mp.mcs_max
update_HB!(mp, phi, costheta, T)
if mcs > discard
ene_per_mcs = observe_ene(mp, phi, costheta)
energy += ene_per_mcs
energy2 += ene_per_mcs^2
end
end
energy /= frac * 2
energy2 /= frac * 4
spec = (energy2 - energy^2) / T^2 / L^2
ave_spec[Tstep] += spec
var_spec[Tstep] += spec^2
ave_ene[Tstep] += energy
var_ene[Tstep] += energy^2
end
end
ave_spec /= runs
var_spec /= runs
ave_ene /= runs
var_ene /= runs
open("E_HB.dat", "w") do fp_E
open("C_HB.dat", "w") do fp_C
for Tstep in 1:Tsteps
T = Ts[Tstep]
write(fp_E, "$T $(ave_ene[Tstep]) $(sqrt((var_ene[Tstep]-ave_ene[Tstep]^2)/(runs-1)))\n")
write(fp_C, "$T $(ave_spec[Tstep]) $(sqrt((var_spec[Tstep]-ave_spec[Tstep]^2)/(runs-1)))\n")
end
end
end
end
function main(ARGS)
L = 4
J1 = 1.0
J2 = 0.0
runs = 5
Tmin = 0.1
Tmax = 2.0
Tsteps = 50
#Tmin=2;Tmax=Tmin;Tsteps=1
mcs_max = 20000
discard = 10000
return main(mp(L, J1, J2, runs, Tmin, Tmax, Tsteps, mcs_max, discard))
end
@main