Scaling of the magnetic linear response in phase-ordering kinetics

TL;DR

This paper investigates the scaling behavior of magnetic responses during phase-ordering in ferromagnets, revealing crossover regimes and deriving relations among critical exponents through theoretical analysis and model testing.

Contribution

It introduces a unified scaling framework for magnetic responses in phase-ordering kinetics and establishes a relation between key exponents based on scaling arguments.

Findings

Identified crossover between two power-law regimes in magnetic response.

Derived a relation connecting exponents a, z, and η.

Validated scaling forms through tests in Glauber-Ising and spherical models.

Abstract

The scaling of the thermoremanent magnetization and of the dissipative part of the non-equilibrium magnetic susceptibility is analysed as a function of the waiting-time $s$ for a simple ferromagnet undergoing phase-ordering kinetics after a quench into the ferromagnetically ordered phase. Their scaling forms describe the cross-over between two power-law regimes governed by the non-equilibrium exponents $a$ and $\lambda_R/z$, respectively. A relation between $a$, the dynamical exponent $z$ and the equilibrium exponent $\eta$ is derived from scaling arguments. Explicit tests in the Glauber-Ising model and the kinetic spherical model are presented.