Partition Function Zeros for Aperiodic Systems

TL;DR

This paper investigates the zeros of partition functions for Ising models on aperiodic structures, revealing insights into critical phenomena beyond traditional periodic systems.

Contribution

It extends the analysis of partition function zeros to aperiodic systems, including Fibonacci chains and tenfold symmetric tilings, using numerical methods.

Findings

Zeros of partition functions are characterized for aperiodic chains.

Analysis reveals unique critical behavior in aperiodic structures.

Numerical methods enable efficient study of complex tilings.

Abstract

The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices. Here, we consider magnetic field and temperature zeros of Ising model partition functions on several aperiodic structures. In 1D, we analyze aperiodic chains obtained from substitution rules, the most prominent example being the Fibonacci chain. In 2D, we focus on the tenfold symmetric triangular tiling which allows efficient numerical treatment by means of corner transfer matrices.