Short-time Dynamic Behaviour of Critical XY Systems

TL;DR

This paper investigates the short-time dynamic scaling behavior of two-dimensional critical XY systems using Monte Carlo methods, revealing universal behavior and differences in dynamic exponents under various conditions.

Contribution

It demonstrates the existence of universal short-time scaling in XY models and identifies violations of standard scaling relations in frustrated systems.

Findings

Universal short-time scaling observed in XY models

Dynamic exponent z varies with initial conditions

Violation of standard scaling relations in frustrated XY models

Abstract

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent $z$ differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.