Local persistense and blocking in the two dimensional Blume-Capel Model

TL;DR

This study investigates local persistence in the 2D Blume-Capel Model, revealing power-law behavior across parameters and identifying blocking phenomena, thus extending understanding of phase dynamics in spin systems.

Contribution

It extends the concept of Glauber dynamics to the 2D Blume-Capel Model, analyzing persistence behavior and discovering universality and blocking effects across different anisotropy ratios.

Findings

Persistence follows a power law for all ratios of D/J.

For negative D/J, the persistence exponent matches the Ising universality class.

Blocking occurs for positive D/J (excluding D/J=1).

Abstract

In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio $\alpha =D/J$ between anisotropy $D$ and exchange $J$ the persistence shows a power law behavior. In particular for $\alpha <0$ we find a persistence exponent $\theta_{l}=0.2096(13)$, \textit{i.e.} in the Ising universality class. For $\alpha >0$ ($\alpha \neq 1$) we observe the occurrence of blocking.