Generalized persistence exponents: an exactly soluble model

TL;DR

This paper introduces and exactly solves a simplified coarsening model with Levy-distributed spin flip intervals, revealing a family of generalized persistence exponents and their distributions.

Contribution

It presents an exactly solvable model of coarsening with Levy-distributed intervals, expanding understanding of generalized persistence exponents in nonequilibrium dynamics.

Findings

Exact expressions for mean magnetization distribution

Derivation of generalized persistence exponents

Identification of Levy law influence on coarsening dynamics

Abstract

It was recently realized that the persistence exponent appearing in the dynamics of nonequilibrium systems is a special member of a continuously varying family of exponents, describing generalized persistence properties. We propose and solve a simplified model of coarsening, where time intervals between spin flips are independent, and distributed according to a L\'evy law. Both the limit distribution of the mean magnetization and the generalized persistence exponents are obtained exactly.