A violation of the Harris-Barghathi-Vojta criterion

TL;DR

This paper presents a topologically disordered lattice that defies the modified Harris-Barghathi-Vojta criterion by maintaining universal behavior despite slow decay of coordination number fluctuations.

Contribution

It demonstrates a violation of the Harris-Barghathi-Vojta criterion in a specific disordered lattice where fluctuations decay slowly yet universal behavior persists.

Findings

Universal behavior preserved despite slow fluctuation decay

Violates the modified Harris criterion in a specific lattice

Challenges the applicability of the Harris-Barghathi-Vojta criterion

Abstract

In 1974, Harris proposed his celebrated criterion: Continuous phase transitions in $d$-dimensional systems are stable against quenched spatial randomness whenever $d\nu>2$, where $\nu$ is the clean critical exponent of the correlation length. Forty years later, motivated by violations of the Harris criterion for certain lattices such as Voronoi-Delaunay triangulations of random point clouds, Barghathi and Vojta put forth a modified criterion for topologically disordered systems: $a\nu >1$, where $a$ is the disorder decay exponent, which measures how fast coordination number fluctuations decay with increasing length scale. Here we present a topologically disordered lattice with coordination number fluctuations that decay as slowly as those of conventional uncorrelated randomness, but for which the universal behaviour is preserved, hence violating even the modified criterion.