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

Physical Review. E
A M FerrenbergD P Landau

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 16^{3} to 1024^{3}. 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 K_{c}=0.221654626(5) and the critical exponent of the correlation length ν=0.629912(86) with precision that exceeds all previous Monte Carlo estimates.

References

Sep 1, 1991·Physical Review. B, Condensed Matter·A M Ferrenberg, D P Landau
Dec 5, 1988·Physical Review Letters·A M Ferrenberg, R H Swendsen
Jan 23, 1989·Physical Review Letters·U Wolff
Sep 18, 1989·Physical Review Letters·A M Ferrenberg, R H Swendsen
Dec 7, 1992·Physical Review Letters·A M FerrenbergY J Wong
Apr 8, 1996·Physical Review Letters·H W BlöteT S Smit
Aug 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Massimo CampostriniEttore Vicari
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Youjin Deng, Henk W J Blöte
Apr 28, 2009·Physical Review Letters·Martin Weigel, Wolfhard Janke
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Martin Weigel, Wolfhard Janke
Jun 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Junfeng WangYoujin Deng

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Citations

May 22, 2019·Physical Review. E·Pengcheng HouYoujin Deng
Jun 20, 2019·Physical Review. E·Yusuke Masumoto, Shinji Takesue
Jun 20, 2019·Physical Review. E·Xiaojun TanJesper Lykke Jacobsen
Dec 2, 2020·Physical Review Letters·Lei ZhangYoujin Deng
Jan 21, 2021·Physical Review. E·Claudio BonatiEttore Vicari
May 16, 2020·Biophysical Journal·Andreana M Rosnik, Phillip L Geissler

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