Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 62: Critical Phenomena and Phase Transitions
DY 62.4: Talk
Friday, March 20, 2020, 10:15–10:30, ZEU 118
Acceptance rate is a thermodynamic function in local Monte Carlo algorithms — Evgeni Burovski1, •Wolfhard Janke2, Maria Guskova1, and Lev Shchur1,3 — 1National Research University Higher School of Economics, 101000 Moscow, Russia — 2Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany — 3Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
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 single-spin-flip algorithms (Metropolis, heat bath) for the one-dimensional Ising chain with periodic boundary conditions. For the Metropolis algorithm we find that the average acceptance rate is a linear function of energy, independent of the chain length. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-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. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.