emilyzinnia / ClassicalSpinMC.jl

Classical spin Monte Carlo

ClassicalSpinMC.jl

This package is for simulating classical spin systems using Monte Carlo (MC) algorithms. It supports arbitrary lattice constructions up to 3 dimensions with any number of basis sites, and Hamiltonians with a Zeeman field, onsite interactions, and up to quartic interaction terms.

Prerequisites

• OpenMPI or IntelMPI. The package uses MPI.jl, so on a cluster you may need to configure your MPI Julia installation to use the system-provided MPI backend. See the MPI.jl documentation for details.
• HDF5

Installation

1. In your desired installation directory, clone the github repository.
2. Launch a Julia REPL and type the following command:

using Pkg; Pkg.add("$INSTALLATION_PATH/ClassicalSpinMC.jl")

where $INSTALLATION_PATH is the path to the package repository.

Usage

The typical workflow is as follows.

1. Define lattice, interaction, and Monte Carlo simulation parameters.
2. Create a UnitCell(a1,...,an) where an are translation vectors.

• Add a basis site using addBasisSite!. Note that some common geometries (e.g. square and honeycomb) are defined in bravais.jl.
• Add Hamiltonian terms using addZeemanCoupling!, addOnSite!, addBilinear!, addCubic! and addQuartic!.

3. Create Lattice object using the UnitCell object, and by specifying the lattice dimensions, spin magnitude, and boundary conditions (default periodic).
4. Initialize MonteCarlo object. If an output path is specified, a .h5 file containing the initial spin configuration and a .h5.params file containing the simulation metadata will be created.
5. Perform the desired MC tasks (e.g. simulated annealing or parallel tempering) to thermalize the system to a desired temperature and take measurements.

Example: Square lattice Heisenberg model with a field

We will first do a simulated annealing example on the square lattice. Import the package and set parameters.

using ClassicalSpinMC
using LinearAlgebra

L = 4 # lattice size
S = 1.0 # spin magnitude 
J = -1.0 .* collect(I(3)) # interaction matrix 
h = 0.1 # Zeeman field strength
h_c = h .* [0., 0., 1.] # Zeeman field vector 
T = 1e-7 # target temperature 
outpath   = string(pwd(), "/")

The Monte Carlo parameters are specified in a dictionary (see the documentation in monte_carlo.jl for details). For simulated annealing, we need to define the number of thermalization sweeps and number of overrelaxation sweeps per Metropolis sweep.

mcparams  = Dict( "t_thermalization" => Int(1e5),     
                  "t_deterministic" => Int(1e6),
                  "overrelaxation"   => 10      )     

Next, generate a unit cell object and add Hamiltonian terms.

UC = Square()  
addBilinear!(S, 1, 1, J, (1, 0)) #x+
addBilinear!(S, 1, 1, J, (-1, 0)) #x-
addBilinear!(S, 1, 1, J, (0, 1 )) #y+
addBilinear!(S, 1, 1, J, (0, -1 )) #y-
addZeemanCoupling!(S, 1, h_c)

Next, we create the lattice object with periodic boundary conditions (by default).

lat = Lattice( (L,L), UC, S, bc="periodic") 

We then initialize and construct the MC object

mc = MonteCarlo(T, lat, mcparams, outpath=outpath)

Because we specified an output path, this line will create configuration.h5.params and configuration_0.h5 files.

Finally, we perform simulated annealing with deterministic updates (used at very low temperatures when the metropolis acceptance rate is almost nonexistent).

simulated_annealing!(mc, x ->1.0*0.9^x, 1.0)
deterministic_updates!(mc)

The current spin configuration is stored in mc.lattice.spins, and can be outputted to configuration_0.h5 using

write_MC_checkpoint(mc)