Universal Window for Two Dimensional Critical Exponents

TL;DR

This paper investigates the distribution of critical exponents in two-dimensional systems, revealing a bounded 'universal window' that challenges existing theories and is explained through numerical and renormalization group analyses.

Contribution

It uncovers a bounded universal window for critical exponents in 2D systems and explains its origin via competition between marginal operators, challenging established critical phenomena theory.

Findings

Distribution of critical exponents is bimodal and bounded between 0.1 and 0.25.

Existing theory cannot fully explain the bounded nature of the exponents.

Universal window arises from competition between marginal operators, as shown by numerical and RG analysis.

Abstract

Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic physics and chemical detail. To unify their physical description is therefore a complex and important challenge. Here we investigate the distribution of experimentally estimated critical exponents, $\beta$, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window $\sim 0.1 \le \beta \le 0.25$, facts that are only in partial agreement with the established theory of critical phenomena. In particular, the bounded nature of the distribution is impossible to reconcile with existing theory for one of the major universality classes of two dimensional behaviour - the XY model with four fold crystal field - which predicts a spectrum of non-universal exponents bounded only from below. Through a combination of numerical and renormalization group arguments we resolve the contradiction between theory and experiment and demonstrate how the "universal window" for critical exponents observed in experiment arises from a competition between marginal operators.