Physical Review Letters

Finite-size scaling of driven diffusive systems: Theory and Monte Carlo studies

Kwan-tai Leung

Published Jan 1, 1991• 104 citations

Abstract

By identifying anisotropic scaling as the dominant feature of a lattice gas driven by a strong electric field, I obtain finite-size scaling forms by extending exact field-theoretic results. These are texted and supplemented by extensive Monte Carlo simulations in two dimensons. Excellent agreements are found. This resolves the disagreements between simulations and theories on the universality of the related models. Novel features of the finite-size effects of intrinsically anisotropic systems are emphasized.

DOI: 10.1103/physrevlett.66.453

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Physical Review Letters

Finite-size scaling of driven diffusive systems: Theory and Monte Carlo studies

Kwan-tai Leung

Published Jan 1, 1991• 104 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.66.453

Related papers

FINITE-SIZE SCALING AT CRITICAL POINTS WITH SPATIAL ANISOTROPIES

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We report some selected recent developments in the finite-size scaling theory of critical phenomena occurring in systems with strong spatial anisotropies. Such systems are characterized by correlation lengths divergent with different exponents (ν⊥, ν||) along different directions. Attention is focused on the driven diffusive lattice gas that exhibits a second order nonequilibrium phase transition. We present in detail the phenomenology and its comparison with computer simulation. Novel features of finite-size effects in anisotropic nonequilibrium systems are emphasized.We report some selected recent developments in the finite-size scaling theory of critical phenomena occurring in systems with strong spatial anisotropies. Such systems are characterized by correlation lengths divergent with different exponents (ν⊥, ν||) along different directions. Attention is focused on the driven diffusive lattice gas that exhibits a second order nonequilibrium phase transition. We present in detail the phenomenology and its comparison with computer simulation. Novel features of finite-size effects in anisotropic nonequilibrium systems are emphasized.

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{\mathit{U}}_{0}

(

{\mathit{tL}}^{\mathit{d}}

)+${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{d}}$

{\mathit{U}}_{1}

(

{\mathit{tL}}^{\mathit{d}}

) with t=1-

{\mathit{T}}_{\mathit{c}}

/T. In particular, we consider the specific heat and Binder's fourth cumulant and show this has a minimum value of 2/3-(

{\mathit{e}}_{1}

{\mathit{e}}_{2}

{\mathit{e}}_{2}

{\mathit{e}}_{1}

{)}^{2}

/12+O(${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{d}}$) at a temperature

{\mathit{T}}_{\mathit{c}}^{(2)}

(L)-

{\mathit{T}}_{\mathit{c}}

=O(${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathit{d}}$). Various other pseudocritical temperatures corresponding to extrema of other cumulants are evaluated. We compare these theoretical predictions with extensive Monte Carlo simulations of the nominally strong first-order transitions in the eight- and ten-state Potts models in two dimensions for system sizes L\ensuremath{\le}50. The ten-state simulations agree with theory in all details in contrast to the eight-state data, and we give estimates for the bulk specific heats at

{\mathit{T}}_{\mathit{c}}

using all exactly known analytic results. A criterion is developed to estimate numerically whether or not system sizes used in a simulation of a first-order transition are in the finite-size-scaling regime.

z = z_{\bot} = z_{\parallel}

. As a consequence, at variance with the claims by the authors, their MC data are not conclusive to determine which one of the field theories proposed in the literature correctly describes the universal properties of the phase transition in these lattice gases.

γ

and

ν

. They turn out to be in perfect agreement with the theoretical predictions. We also compute the transverse Binder parameter, which apparently vanishes at the critical point, and the distribution of the magnetization. These results confirm the Gaussian nature of the transverse excitations.