Dynamic critical behavior of the XY model in small-world networks

TL;DR

This paper investigates the critical behavior of the XY model on small-world networks using dynamic Monte Carlo simulations, revealing mean-field universality and independence of the dynamic critical exponent from rewiring probability.

Contribution

It introduces a dynamic finite-size scaling analysis of the XY model on small-world networks and identifies the universality class and exponent independence.

Findings

Dynamic universality class is mean-field.

Dynamic critical exponent is independent of rewiring probability P for P > 0.03.

Critical behavior studied via nonequilibrium relaxation from short-time dynamics.

Abstract

The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for P > 0.03.