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https://github.com/yomichi/SpinMonteCarlo.jl
Markov chain Monte Carlo solver for lattice spin systems implemented in Julialang
https://github.com/yomichi/SpinMonteCarlo.jl
ising-model julialang lattice mcmc monte-carlo physics quantum-physics spin statistical-physics
Last synced: 2 months ago
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Markov chain Monte Carlo solver for lattice spin systems implemented in Julialang
- Host: GitHub
- URL: https://github.com/yomichi/SpinMonteCarlo.jl
- Owner: yomichi
- License: mit
- Created: 2016-10-06T12:10:01.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2024-03-17T09:48:42.000Z (3 months ago)
- Last Synced: 2024-04-17T10:37:38.377Z (2 months ago)
- Topics: ising-model, julialang, lattice, mcmc, monte-carlo, physics, quantum-physics, spin, statistical-physics
- Language: Julia
- Homepage: https://yomichi.github.io/SpinMonteCarlo.jl/latest/
- Size: 702 KB
- Stars: 42
- Watchers: 3
- Forks: 7
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Lists
- awesome-stars - yomichi/SpinMonteCarlo.jl - Markov chain Monte Carlo solver for lattice spin systems implemented in Julialang (Julia)
README
# SpinMonteCarlo.jl
Markov chain Monte Carlo solver for finite temperature problem of lattie spin system implemented by [Julia](https://julialang.org) language.
[Online manual](https://yomichi.github.io/SpinMonteCarlo.jl/latest)
# Install
``` julia
Pkg> add SpinMonteCarlo
```
# Simple example
[The following program](example/simple.jl) calculates temperature v.s. specific heat of the ferromagnetic Ising model on a $16\times 16$ square lattice by Swendsen-Wang algorithm.
``` julia
using SpinMonteCarlo
using Printf
const model = Ising
const lat = "square lattice"
const L = 16
const update = SW_update!
const Tc = 2.0/log1p(sqrt(2))
const Ts = Tc*range(0.85, stop=1.15, length=31)
const MCS = 8192
const Therm = MCS >> 3
for T in Ts
params = Dict{String,Any}("Model"=>model, "Lattice"=>lat,
"L"=>L, "T"=>T, "J"=>1.0,
"Update Method"=>update,
"MCS"=>MCS, "Thermalization"=>Therm,
)
result = runMC(params)
@printf("%f %.15f %.15f\n",
T, mean(result["Specific Heat"]), stderror(result["Specific Heat"]))
end
```
# Implemented
## Model
- Classical spin model
- `Ising` model
- `Q` state `Potts` model
- order parameter defined as $M = n_1(Q-1)/Q - (1-n_1)/Q$, where $n_1$ is the number density of $q=1$ spins.
- `XY` model
- `Q` state `Clock` model
- `AshkinTeller` model
- Quantum spin model
- spin-`S` `QuantumXXZ` model
- $\mathcal{H} = \sum_{ij} [ Jz_{ij} S_i^z S_j^z + \frac{Jxy_{ij}}{2} (S_i^+ S_j^- + S_i^-S_j^+) ] - \sum_i \Gamma_i S_i^x$
## Lattice
- `chain lattice`
- `L`
- `bond-alternating chain lattice`
- `L`
- `square lattice`
- `L * W`
- `J1J2 square lattice`
- `L * W`
- `triangular lattice`
- `L * W`
- `cubic lattice`
- `L * W * H`
- `fully connected graph`
- `N`
## Update algorithm
- Classical spin
- `local_update!`
- `SW_update!`
- `Wolff_update!`
- Quantum spin
- `loop_update!`
## Physical quantities
- `Ising`, `Potts`
- `Magnetization`
- $\braket{m} := \braket{ M_\text{total}/N_\text{site} }$
- `|Magnetization|`
- $\braket{|m|} := \braket{|M_\text{total}/N_\text{site}|}$
- `Magnetization^2`
- $\braket{m^2} := \braket{(M_\text{total}/N_\text{site})^2}$
- `Magnetization^4`
- $\braket{m^4} := \braket{(M_\text{total}/N_\text{site})^4 }$
- `Binder Ratio`
- $U_{4,2} := \braket{m^4}/\braket{m^2}^2$
- `Susceptibility`
- $\chi := \partial_h \braket{m} = (N/T)(\braket{m^2} - \braket{m}^2)$
- `Connected Susceptibility`
- $\chi := (N/T)(\braket{m^2} - \braket{|m|}^2)$
- `Energy`
- $E := \braket{\mathcal{H}} = \braket{E_\text{total}}/N_\text{site}$
- `Energy^2`
- $E^2 := \braket{\mathcal{H}^2}$
- `Specific Heat`
- $C := \partial_\beta \braket{\mathcal{H}} = (N/T^2)(\braket{\mathcal{H}^2} - \braket{\mathcal{H}}^2)$
- `XY`, `Clock`
- `|Magnetization|`
- `|Magnetization|^2`
- `|Magnetization|^4`
- `Binder Ratio`
- `Susceptibility`
- `Connected Susceptibility`
- `Magnetization x`
- `|Magnetization x|`
- `Magnetization x^2`
- `Magnetization x^4`
- `Binder Ratio x`
- `Susceptibility x`
- `Connected Susceptibility x`
- `Magnetization y`
- `|Magnetization y|`
- `Magnetization y^2`
- `Magnetization y^4`
- `Binder Ratio y`
- `Susceptibility y`
- `Connected Susceptibility y`
- `Helicity Modulus x`
- `Helicity Modulus y`
- `Energy`
- `Energy^2`
- `Specific Heat`
- `QuantumXXZ`
- `Magnetization`
- $\braket{m} := \braket{\sum_i S_i^z } / N_\text{site}$
- `Magnetization^2`
- $\braket{m^2}:= \braket{(\sum_i S_i^z)^2 } / N_\text{site}^2$
- `Magnetization^4`
- $\braket{m^4}:= \braket{(\sum_i S_i^z)^4 } / N_\text{site}^4$
- `Binder Ratio`
- $U_{4,2} := \braket{m^4}/\braket{m^2}^2$
- `Susceptibility`
- $\chi := \partial_h \braket{m} = (N/T)(\braket{m^2} - \braket{m}^2)$
- `Energy`
- $E := \braket{\mathcal{H}}$
- `Energy^2`
- $E^2 := \braket{\mathcal{H}^2}$
- `Specific Heat`
- $C := \partial_\beta \braket{\mathcal{H}} = (N/T^2)(\braket{\mathcal{H}^2} - \braket{\mathcal{H}}^2)$
# Future work
- `Model`
- Classical model
- Heisenberg model
- antiferro interaction
- magnetic field
- Quantum model
- SU(N) model
- `Update Method`
- worm algorithm
- Others
- random number parallelization
- NOTE: parameter parallelization can be realized simply by using `@parallel for` or `pmap`.
- write algorithmic note
- especially, Foutuin-Kasteleyn representaion and improved estimators
# Author
[Yuichi Motoyama](https://github.com/yomichi), the University of Tokyo, 2016-
This package is distributed under the MIT license.