Renormalization of Systems with Non-equilibrium Critical Stationary States

TL;DR

This paper introduces a new renormalization method tailored for non-equilibrium systems with steady-states, enabling the analysis of their critical properties and phase transition behavior.

Contribution

It presents the Dynamically Driven Renormalization Group, a novel approach for studying non-equilibrium critical phenomena through coarse-grained time evolution.

Findings

Derived recursion relations for model parameters under scale change

Calculated critical exponents for non-equilibrium systems

Applied framework to models exhibiting self-organized criticality

Abstract

We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution operator by computing the rescaled time transition rate between coarse grained states. The obtained renormalization equations are coupled to a stationarity condition which provides the approximate non-equilibrium statistical weights of steady-state configurations to be used in the calculations. In this way we are able to write recursion relations for the parameters evolution under scale change, from which we can extract numerical values for the critical exponents. This general framework allows the systematic analysis of several models showing self-organized criticality in terms of usual concepts of phase transitions and critical phenomena.