Critical Dynamics: multiplicative noise fixed point in two dimensional systems

TL;DR

This paper investigates the critical dynamics of a two-dimensional scalar field near phase transition, revealing a novel multiplicative noise fixed point that defines a new universality class distinct from higher-dimensional cases.

Contribution

It introduces and analyzes a new multiplicative noise fixed point in 2D critical dynamics, expanding understanding beyond the Wilson-Fisher fixed point in higher dimensions.

Findings

Discovered a multiplicative noise fixed point dominating 2D critical dynamics.

Critical exponents are universal, independent of stochastic prescription.

Different stochastic prescriptions lead to the same universality class.

Abstract

We study the critical dynamics of a real scalar field in two dimensions near a continuous phase transition. We have built up and solved Dynamical Renormalization Group equations at one-loop approximation. We have found that, different form the case $d\lesssim 4$, characterized by a Wilson-Fisher fixed point with dynamical critical exponent $z=2+ O(\epsilon^2)$, the critical dynamics is dominated by a novel multiplicative noise fixed point. The zeroes of the beta function depend on the stochastic prescription used to define the Wiener integrals. However, the critical exponents and the anomalous dimension do not depend on the prescription used. Thus, even though each stochastic prescription produces different dynamical evolutions, all of them are in the same universality class.