• Editors' Suggestion

Acceptance rate is a thermodynamic function in local Monte Carlo algorithms

Evgeni Burovski, Wolfhard Janke, Maria Guskova, and Lev Shchur
Phys. Rev. E 100, 063303 – Published 10 December 2019

Abstract

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 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 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 15 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.063303

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

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

  • *lev@landau.ac.ru

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 100, Iss. 6 — December 2019

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×