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Regular version of the site

Working paper

Acceptance rate is a thermodynamic function in local Monte Carlo algorithms

arxiv.org. cond-mat. Cornell University, 2019. No. arXiv:1907.06776.
Burovski E., Janke W., Гуськова М. С., Shchur L.
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of the single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the 3- and 4-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat.