Microcanonical Transfer Matrix and Yang-Lee Zeros of the Q-State Potts Model
Richard J. Creswick, Seung-Yeon Kim (University of South Carolina, at Columbia)
TL;DR
This paper introduces a microcanonical transfer matrix approach to analyze the distribution of partition function zeros in the complex plane for the Ising and Potts models, providing exact finite-lattice results.
Contribution
It presents a novel method using the microcanonical transfer matrix to compute exact partition functions and analyze Yang-Lee zeros for finite two-dimensional lattice models.
Findings
Density of zeros in complex x-plane for Ising model at specific y-values
Density of zeros in complex y-plane for three-state Potts model
Exact finite-lattice partition function calculations
Abstract
The microcanonical transfer matrix and its extensions offer a new way of obtaining exact partition functions on finite two dimensional lattices. We show the density of the partition function zeros in the complex x- plane for the Ising model at and , and the density of the partition function zeros in the complex y-plane for the three-state Potts model.
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Taxonomy
TopicsRandom Matrices and Applications · Theoretical and Computational Physics · Quantum many-body systems