Ising spins on the labyrinth

TL;DR

This paper investigates the critical behavior of Ising spins on a quasiperiodic Labyrinth tiling, revealing universality class characteristics and analyzing magnetization through duality and Monte Carlo methods.

Contribution

It provides exact critical behavior insights for a quasiperiodic Ising model and explores the magnetization in generic cases using Monte Carlo simulations.

Findings

Critical behavior belongs to the Onsager universality class

Magnetization is position-independent in certain models

Monte Carlo results extend understanding to generic couplings

Abstract

We consider a zero-field Ising model defined on a quasiperiodic graph, the so-called Labyrinth tiling. Exact information about the critical behaviour is obtained from duality arguments and the subclass of models which yield commuting transfer matrices. For the latter, the magnetization is independent of the position and the phase transition between ordered and disordered phase belongs to the Onsager universality class. In order to obtain information about the generic case, we calculate the magnetization for a series of couplings by standard Monte-Carlo methods.