From surface to random criticality in layered planar Ising models

TL;DR

This paper analyzes a layered planar Ising model with nonuniform layers using an exact renormalization group, revealing multiple universality classes and providing new insights into random criticality.

Contribution

It introduces a unified theoretical framework to study various surface, finite size, quasiperiodic, and random universality classes in layered Ising models.

Findings

Identifies multiple universality classes in layered Ising models.

Provides exact analysis of random criticality.

Unifies different critical behaviors within a single framework.

Abstract

A general case of a spatially nonuniform planar layered Ising model, or an equivalent quantum Ising chain, is analysed with an exact functional real space renormalization group. Various surface, finite size, quasiperiodic and random layer (McCoy-Wu) universality classes are obtained and discussed within a single theoretical framework leading to new insights into the nature of random criticality.