Persistence Exponents and Scaling In Two Dimensional XY model and A Nematic Model

TL;DR

This study numerically evaluates the persistence exponents during zero-temperature quenching in 2D XY and nematic models, revealing distinct decay rates and confirming that persistence correlations scale with domain growth.

Contribution

It provides the first numerical estimates of persistence exponents for these models and analyzes the scaling behavior of persistent sites during phase ordering.

Findings

Persistence exponents are 0.305 for XY and 0.199 for nematic models.

Persistence correlation length scales with the domain length L(t).

Persistence probability decays as L(t)^-theta over time.

Abstract

The persistence exponents associated with the T=0 quenching dynamics of the two dimensional XY model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation. The site persistence or the probability that the sign of a local spin component does not change starting from initial time t=0 up to certain time t, is found to decay as L(t)^-theta, (L(t) is the linear domain length scale), with theta =0.305 for the two dimensional XY model and 0.199 for the two dimensional uniaxial spin nematic model. We have also investigated the scaling (at the late time of phase ordering) associated with the correlated persistent sites in both models. The persistence correlation length was found to grow in same way as L(t).