Distribution and density of the partition function zeros for the diamond-decorated Ising model

TL;DR

This paper analyzes the distribution of partition function zeros in the complex temperature plane for a decorated Ising model, revealing how these distributions evolve with decoration level and their connection to Julia sets.

Contribution

It provides an exact renormalization map for temperature and characterizes the distribution and density of zeros across decoration levels, including conjectures for higher levels.

Findings

Distribution pattern of zeros varies with decoration level

Explicit density calculations for first two levels

Connection between zeros distribution and Julia sets

Abstract

Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the variation of the distribution pattern as the decoration-level changes is given. The densities of the zeros for the first two decoration-levels are calculated explicitly, and the qualitative features about the densities of higher decoration-levels are given by conjecture. The Julia set associated with the renormalization map is contained in the distribution of the zeros in the limit of infinite decoration level, and the formation of the Julia set in the course of increasing the decoration-level is given in terms of the variations of the zero density.