Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

Alan M. Ferrenberg, Jiahao Xu, and David P. Landau
Phys. Rev. E 97, 043301 – Published 4 April 2018

Abstract

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221654626(5) and the critical exponent of the correlation length ν=0.629912(86) with precision that exceeds all previous Monte Carlo estimates.

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  • Received 19 May 2017
  • Revised 28 February 2018

DOI:https://doi.org/10.1103/PhysRevE.97.043301

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Alan M. Ferrenberg1,*, Jiahao Xu2, and David P. Landau2,†

  • 1Information Technology Services and Department of Chemical, Paper & Biomedical Engineering, Miami University, Oxford, Ohio 45056, USA
  • 2Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA

  • *alan.ferrenberg@miamioh.edu
  • dlandau@physast.uga.edu

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Issue

Vol. 97, Iss. 4 — April 2018

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