Dynamic Renormalization Group Study of the $\phi^4$ Model with Colored Noise

TL;DR

This study uses Dynamic Renormalization Group analysis to examine how colored noise influences the critical behavior of the non-conserved $$ model, revealing shifts in critical points without altering critical exponents.

Contribution

It provides a theoretical analysis of the $$ model with colored noise, showing the effects of noise correlation time and length on critical points while confirming previous numerical findings.

Findings

Correlation time shifts the critical point location.

Correlation length of noise also affects the critical point.

Critical exponents remain unchanged up to order ^2.

Abstract

The non-conserved $\phi^4$ model defined by a Langevin equation with external non-white noise is studied by means of the Dynamic Renormalization Group. The correlation time of the noise changes the critical point location but does not affect the critical exponents up to order $\varepsilon^2$. The same effect is obtained when the correlation length of the noise is considered. These results are shown to be in agreement with previous numerical simulations.