A Monte Carlo Renormalization-Group Study of Criticality in Anisotropic Driven Lattice Gases Using the Shannon Entropy

George L. Daquila, Uwe Claus Täuber

We employ Monte Carlo simulations to study the nonequilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density autocorrelation function in the nonequilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time autocorrelations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.

Tom Kennedy

Yantao Wu, Roberto Car

We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. We study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.

Gustavo P. Saracco, M. Leticia Rubio Puzzo, M. A. Bab

Kurt Binder, Erik Luijten

Sergio Caracciolo A, Andrea Gambassi, Massimiliano Gubinelli +1 more

In a recent Letter Albano and Saracco study the dynamic critical behavior of some anisotropic driven lattice gases by Monte Carlo (MC) simulations. In this Comment we point out that the Ansätze they use to relate the measured scaling exponents with the critical exponents analytically computed within different field-theoretical approaches do not take properly into account the strongly anisotropic nature of the phase transition, by implicitly assuming $z = z_{\bot} = z_{\parallel}$. 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.