The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

Delft University of Technology; H.W.J. Bl\"ote (Department of Applied Physics; Kingston; M. P. Nightingale (Department of Physics; RI); the Netherlands); University of Rhode Island

The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

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arxiv cond-mat/9601059 v2 pith:6E2A4PEO submitted 1996-01-16 cond-mat

M. P. Nightingale (Department of Physics , University of Rhode Island , Kingston , RI) , H.W.J. Blöte (Department of Applied Physics , Delft University of Technology , The Netherlands) This is my paper · ORCID

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keywords timesautocorrelationcarloexponentisingmethodmontetwo-dimensional

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abstract

We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random site selection and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these autocorrelation times, the dynamical critical exponent $z$ is determined as $z=2.1665$ (12).

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The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model
cond-mat.stat-mech 2019-08 conditional novelty 5.0 of 10

Monte Carlo simulations of the improved Blume-Capel model give the dynamic critical exponent of the 3D Ising universality class as z = 2.0245(15).

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