Large deviations for the skew-detailed-balance lifted-Markov processes to sample the equilibrium distribution of the Curie–Weiss model
Cécile Monthus
Abstract
Abstract Among the Markov chains breaking detailed-balance that have been proposed in the field of Monte-Carlo sampling in order to accelerate the convergence towards the steady state with respect to the detailed-balance 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 skew-detailed-balance lifted-Markov-chain introduced by Turitsyn et al (2011 Physica D 240 410) is revisited for the Curie–Weiss mean-field ferromagnetic model, where the dynamics for the magnetization is closed. The large deviations at various levels for empirical time-averaged observables are analyzed and compared with their detailed-balance counterparts, both for the discrete extensive magnetization M and for the continuous intensive magnetization <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> </mml:mfrac> </mml:math> for large system-size N .