Numerical tests confirm the shaken dynamics reproduces the predicted Ising phase transition curve, while mixing-time and GPU benchmark results support its use as a fast parallel sampler.
Shaken dynamics: an easy way to parallel Markov Chain Monte Carlo
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abstract
We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function $H(\sigma)$. These dynamics turn out to be reversible and their stationary measure is explicitly determined. Convergence to equilibrium and relation of the stationary measure to the usual Gibbs measure are discussed when the dynamics is defined on $\mathbb{Z}^2$. Further it is shown how these dynamics can be used to define natively parallel algorithms to face problems in the context of combinatorial optimization.
fields
physics.comp-ph 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Parallel simulation of two--dimensional Ising models using Probabilistic Cellular Automata
Numerical tests confirm the shaken dynamics reproduces the predicted Ising phase transition curve, while mixing-time and GPU benchmark results support its use as a fast parallel sampler.