Landau like theory for universality of critical exponents in quasistatioary states of isolated mean-field systems

TL;DR

This paper develops a Landau-like theoretical framework to compute critical exponents in quasistationary states of isolated mean-field systems, extending universality and scaling relations beyond previous models.

Contribution

It introduces a unified method for calculating critical exponents in quasistationary states, generalizing their universality class to spatially periodic one-dimensional systems.

Findings

Provides a simple Landau-like theory for critical exponents.

Extends universality of non-classical exponents to 1D spatially periodic systems.

Shows exponents satisfy classical scaling relations via momentum scaling.

Abstract

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two non-classical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends universality class of the non-classical exponents to spatially periodic one-dimensional systems, and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.