Global persistence exponent of the double-exchange model

TL;DR

This paper calculates the global persistence exponent for a continuous spin double-exchange model on a cubic lattice using two methods, confirming consistent results and advancing understanding of its dynamic critical behavior.

Contribution

It introduces two methods to estimate the global persistence exponent in the double-exchange model and demonstrates their agreement, providing new insights into its critical dynamics.

Findings

Consistent estimates of the global persistence exponent $ heta_g$ using two methods.

Validation of the universal scaling collapse for different lattice sizes.

Enhanced understanding of the dynamic critical behavior of the double-exchange model.

Abstract

We obtained the global persistence exponent $\theta_g$ for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent $\theta_g$ by following the time evolution of probability $P(t)$ that the order parameter of the model does not change its sign up to time $t$ $[P(t)\thicksim t^{-\theta_g}]$. Afterwards, that exponent was estimated through the scaling collapse of the universal function $L^{\theta_g z} P(t)$ for different lattice sizes. Our results for both approaches are in very good agreement each other.