PMID: 22587077May 17, 2012Paper

Universality of the Ising and the S=1 model on Archimedean lattices: a Monte Carlo determination

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Anastasios MalakisG Aslan

Abstract

The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.

References

Jun 1, 1986·Physical Review. B, Condensed Matter·D P Landau, R H Swendsen
Feb 1, 1986·Physical Review. B, Condensed Matter·P D Beale
Oct 1, 1988·Physical Review. B, Condensed Matter·J B CollinsE T Gawlinski
Sep 1, 1991·Physical Review. B, Condensed Matter·A M Ferrenberg, D P Landau
Jan 12, 1987·Physical Review Letters·R H Swendsen, J S Wang
Jan 23, 1989·Physical Review Letters·U Wolff
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, Chin-Kun Hu
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P N Suding, R M Ziff
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A MalakisN G Fytas
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ming-Chya WuN Sh Izmailian
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C J SilvaJ A Plascak
Apr 12, 2006·Physical Review Letters·R KennaW Janke
May 23, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christian R Scullard, Robert M Ziff
Dec 13, 2006·Physical Review Letters·R KennaW Janke
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A MalakisN G Fytas
May 21, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A MalakisT Papakonstantinou
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Elmar Bittner, Wolfhard Janke

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Citations

Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A MalakisT Papakonstantinou
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T Papakonstantinou, A Malakis
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ana L Acuña-LaraJosé Raúl Vargas-Arriola
Mar 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N J ZhouJ H Dai

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