Large deviations for the skewdetailedbalance liftedMarkov processes to sample the equilibrium distribution of the CurieWeiss model
Abstract
Among the Markov chains breaking detailedbalance that have been proposed in the field of MonteCarlo sampling in order to accelerate the convergence towards the steady state with respect to the detailedbalance dynamics, the idea of 'lifting' consists in duplicating the configuration space into two copies σ = ± and in imposing directed flows in each copy in order to explore the configuration space more efficiently. The skewdetailedbalance liftedMarkovchain introduced by Turitsyn et al (2011 Physica D 240 410) is revisited for the CurieWeiss meanfield ferromagnetic model, where the dynamics for the magnetization is closed. The large deviations at various levels for empirical timeaveraged observables are analyzed and compared with their detailedbalance counterparts, both for the discrete extensive magnetization M and for the continuous intensive magnetization $m=\frac{M}{N}$ for large systemsize N.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 October 2021
 DOI:
 10.1088/17425468/ac22f9
 arXiv:
 arXiv:2106.09429
 Bibcode:
 2021JSMTE2021j3202M
 Keywords:

 classical Monte Carlo simulations;
 first passage;
 large deviations in nonequilibrium systems;
 stationary states;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 v3=final version (40 pages)