Abstract
AbstractWe define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function $$H(\sigma )$$
H
(
σ
)
. 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 $$\mathbb {Z}^2$$
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.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference21 articles.
1. Apollonio, V., D’Autilia, R., Scoppola, B., Scoppola, E., Troiani, A.: Criticality of measures on 2-d Ising configurations: from square to hexagonal graphs. J. Stat. Phys. 177(5), 1009–1021 (2019)
2. Apollonio, V., Jacquier, V., Nardi, F.R., Troiani, A.: Metastability for the Ising model on the hexagonal lattice. Electron. J. Probab. 27, 1–48 (2022)
3. Bovier, A., Den Hollander, F.: Metastability: A Potential-Theoretic Approach, vol. 351. Springer, Berlin (2016)
4. Cimasoni, D., Duminil-Copin, H.: The critical temperature for the Ising model on planar doubly periodic graphs. Electron. J. Probab. 18, 1–18 (2013)
5. Cirillo, E.N.M.: A note on the metastability of the Ising model: the alternate updating case. J. Stat. Phys. 106(1), 385–390 (2002)
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