The Glauber-Ising chain under low-temperature protocols

TL;DR

This paper analyzes the low-temperature dynamics of the Glauber-Ising chain under various temperature protocols, focusing on domain wall density and susceptibility to understand domain growth and non-equilibrium behavior.

Contribution

It introduces a comprehensive framework to study domain growth and pattern formation in the Glauber-Ising chain under diverse temperature protocols at low temperatures.

Findings

Derived a dimensionless form factor characterizing domain patterns.

Analyzed effects of slow quenches and periodic protocols on domain growth.

Explored memory effects in two-temperature protocols.

Abstract

This work is devoted to an in-depth analysis of arbitrary temperature protocols applied to the ferromagnetic Glauber-Ising chain launched from a disordered initial state and evolving in the low-temperature scaling regime. We focus our study on the density of domain walls and the reduced susceptibility. Both the inverse of the former observable and the latter one provide two independent measures of the typical size of the growing ferromagnetic domains. Their product is thus a dimensionless form factor characterising the pattern of growing ordered domains and providing a measure of the distance of the system to thermal equilibrium. We apply this framework to a variety of protocols: everlasting slow quenches, where temperature decreases continuously to zero in the limit of infinitely long times, slow quenches of finite duration, where temperature reaches zero at some long but finite quenching time, time-periodic protocols with weak and strong modulations, and the two-temperature protocol leading to the memory effect found by Kovacs.