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arXiv:hep-lat/9207007 · International Journal of Modern Physics C

RECENT RESULTS OF MULTIMAGNETICAL SIMULATIONS OF THE ISING MODEL

Ulrich H. E. Hansmann, Bernd A. Berg, T. Neuhaus

Published Oct 1, 1992• 8 citations
arXivHTMLPDF

Abstract

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D and 3D Ising model. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D results. In the physically more interesting 3D case we estimate the amplitude [Formula: see text] of the critical interfacial tension.

DOI
10.1142/s0129183192000786

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To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D and 3D Ising model. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D results. In the physically more interesting 3D case we estimate the amplitude [Formula: see text] of the critical interfacial tension.
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In order to reduce the critical slowing down in Monte Carlo simulations, a numerical study for the Ising model on 3-D random lattice using Swendsen-Wang algorithm is performed. The critical point obtained is βc=0. 075±0. 001. Moreover, to analyse the dynamical property of Swendsen-Wang method, the dynamical critical exponent z is estimated. The result is z =0. 74 ±0. 03. This indicates that the Swendsen-Wang method can greatly reduce the critical slowing down for the Ising model on 3-D random lattice.
With recent improvements in simulation methods and data analysis techniques, Monte Carlo simulations, used in conjunction with finite-size scaling techniques, have become the most powerful and flexible tools for studying critical phenomena. In particular, there has been a dramatic increase in resolution in studies of the three-dimensional Ising model. This paper discusses motivations for performing high-resolution studies, reviews past and current work on the model and points out some potential potholes on the road to higher resolution.
In order to reduce the critical slowing down in Monte Carlo simulations, a numerical study for the Ising model on 3-D random lattice using Swendsen-Wang algorithm is performed. The critical point obtained isβc=0. 075?. 001. Moreover, to analyse the dynamical property of Swendsen-Wang method, the dynamical critical exponent z is estimated. The result is z =0. 74 ±0. 03. This indicates that the Swendsen-Wang method can greatly reduce the critical slowing down for the Ising model on 3-D random lattice.