Revisiting a Low-Dimensional Model with Short Range Interactions and Mean Field Critical Behavior

TL;DR

This paper demonstrates that a specific non-equilibrium low-dimensional model exhibits exact mean field critical behavior, with deviations being non-leading corrections, supported by high-statistics simulations in 2D and 3D.

Contribution

It provides high-precision simulation evidence that this model's critical exponents are exactly mean field, clarifying the role of phase randomization in non-equilibrium systems.

Findings

Critical exponents match mean field predictions.

Deviations from mean field are non-leading corrections.

Scaling behavior is precisely mean field in 2D and 3D.

Abstract

In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior is an inherently non-equilibrium model studied some time ago by H.-M. Broker and myself. In simulations, its 2-dimensional version suggested that two critical exponents were mean-field, while a third one showed very small deviations. Moreover, the numerics agreed almost perfectly with an explicit mean field model. In the present paper we present simulations with much higher statistics, both for 2d and 3d. In both cases we find that the deviations of all critical exponents from their mean field values are non-leading corrections, and that the scaling is {\it precisely} of mean field type. As in the original paper, we propose that the mechanism for this is ``confusion", a strong randomization of the phases of feed-backs that can occur in non-equilibrium systems.