Non-Analytic Non-Equilibrium Field Theory: Stochastic Reheating of the Ising Model

TL;DR

This paper develops a non-analytic field theory framework to describe non-equilibrium steady states, specifically analyzing how stochastic reheating affects the Ising model and leads to new fixed points.

Contribution

It introduces non-analytic terms into Landau-Ginzburg theory for non-equilibrium states and demonstrates their relevance through RG analysis and simulations.

Findings

Non-analytic operators deform the potential in non-equilibrium steady states.

Stochastic reheating destabilizes the equilibrium fixed point.

A new non-equilibrium fixed point is identified.

Abstract

Many-body non-equilibrium steady states can be described by a Landau-Ginzburg theory if one allows non-analytic terms in the potential. We substantiate this claim by working out the case of the Ising magnet in contact with a thermal bath and undergoing stochastic reheating: It is reset to a paramagnet at random times. By a combination of stochastic field theory and Monte Carlo simulations, we unveil how the usual $\varphi^4$ potential is deformed by non-analytic operators of intrinsic non-equilibrium nature. We demonstrate their infrared relevance at low temperatures by a renormalization-group analysis of the non-equilibrium steady state. The equilibrium ferromagnetic fixed point is thus destabilized by stochastic reheating, and we identify the new non-equilibrium fixed point.