Critical Relaxation and Critical Exponents

TL;DR

This paper investigates the dynamic relaxation behavior of XY models at criticality using Monte Carlo simulations, revealing universal scaling laws and extracting critical exponents with results comparable to traditional methods.

Contribution

It provides a novel analysis of dynamic relaxation in XY models at critical points using Monte Carlo methods, focusing on universal scaling and critical exponents.

Findings

Universal power law scaling observed during relaxation.

Critical exponents $z$ and $ta$ successfully extracted.

Results are competitive with traditional measurement techniques.

Abstract

Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The dynamic critical exponent $z$ and the static exponent $\eta$ are extracted from the time-dependent Binder cumulant and magnetization. The results are competitive to those measured with traditional methods.