Critical behavior of an Ising model with aperiodic interactions

TL;DR

This paper investigates how aperiodic interactions affect the critical behavior of the Ising model on a hierarchical lattice, revealing stability for small fluctuations and instability for large ones, with a heuristic criterion for fluctuation relevance.

Contribution

It provides exact renormalization-group recursion relations for the Ising model with aperiodic interactions and analyzes the impact of geometric fluctuations on critical behavior.

Findings

Critical behavior remains unchanged for small fluctuations.

Large fluctuations destabilize the uniform fixed point.

A heuristic criterion predicts the relevance of fluctuations.

Abstract

We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, the uniform fixed point in the parameter space becomes fully unstable. We analyze some limiting cases, and propose a heuristic criterion to check the relevance of the fluctuations.