Cluster statistics of critical Ising and Ashkin-Teller models

Fuente: arXiv
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Main Authors: Xu, Zhaonian, Yu, Rong
Format: Preprint
Published: 2024
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author Xu, Zhaonian
Yu, Rong
author_facet Xu, Zhaonian
Yu, Rong
contents Motivated by recent progress on the scaling behavior of entanglement entropy, we study the scaling behavior of the number of clusters crossing the boundary between two subsystems for several classical statistical models in two dimension. This number exhibits a subleading logarithmic dependence of the linear dimension of the boundary when the model is at critical, in analogy to the entanglement entropy of a quantum system. It is shown that the logarithmic scaling of the cluster number originates from the conformal invariance of the critical system. We check this numerically for Ising and Ashkin-Teller models by using Monte Carlo simulations, and show that whether a universal coefficient of the logarithmic term can be observed numerically may strongly depend on the geometry and boundary condictions of the system.
format Preprint
id arxiv_https___arxiv_org_abs_2405_05747
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Cluster statistics of critical Ising and Ashkin-Teller models
Xu, Zhaonian
Yu, Rong
Statistical Mechanics
Strongly Correlated Electrons
Motivated by recent progress on the scaling behavior of entanglement entropy, we study the scaling behavior of the number of clusters crossing the boundary between two subsystems for several classical statistical models in two dimension. This number exhibits a subleading logarithmic dependence of the linear dimension of the boundary when the model is at critical, in analogy to the entanglement entropy of a quantum system. It is shown that the logarithmic scaling of the cluster number originates from the conformal invariance of the critical system. We check this numerically for Ising and Ashkin-Teller models by using Monte Carlo simulations, and show that whether a universal coefficient of the logarithmic term can be observed numerically may strongly depend on the geometry and boundary condictions of the system.
title Cluster statistics of critical Ising and Ashkin-Teller models
topic Statistical Mechanics
Strongly Correlated Electrons
url https://arxiv.org/abs/2405.05747