Lee-Yang zeros and the Ising model on the Sierpinski Gasket

TL;DR

This paper investigates the distribution of Lee-Yang zeros for the Ising model on a Sierpinski gasket, revealing how zeros approach the real axis and explaining low-temperature behavior similarities with linear chains.

Contribution

It provides an exact recursive analysis of Lee-Yang zeros on a fractal lattice, uncovering their asymptotic density behavior near the origin.

Findings

Zeros form a curve pinching the real axis at T=0

Density of zeros vanishes asymptotically along the curve

Explains low-temperature regime similarity with linear chain

Abstract

We study the distribution of the complex temperature zeros for the partition function of the Ising model on a Sierpinski gasket using an exact recursive relation. Although the zeros arrange on a curve pinching the real axis at T=0 in the thermodynamic limit, their density vanishes asymptotically along the curve approaching the origin. This phenomenon explains the coincidence of the low temperature regime on the Sierpinski gasket and on the linear chain.