Effect of Random Impurities on Fluctuation-Driven First Order Transitions

TL;DR

This paper investigates how quenched randomness influences fluctuation-driven first order phase transitions in coupled Ising models, showing that weak randomness can stabilize the transition and restore critical behavior.

Contribution

It demonstrates that weak quenched randomness can stabilize runaway RG flows in coupled Ising models, restoring second-order criticality in two dimensions.

Findings

Weak randomness stabilizes RG flows towards pure Ising fixed point.

Transitions in higher dimensions may become continuous or stay first order with randomness.

Pure models exhibit fluctuation-driven first order transitions for N>2.

Abstract

We analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of N coupled two-dimensional Ising models. For N>2 the pure model exhibits a fluctuation-driven first order transition, characterised by runaway renormalisation group behaviour. We show that the addition of weak randomness acts to stabilise these flows, in such a way that the trajectories ultimately flow back towards the pure decoupled Ising fixed point, with the usual critical exponents alpha=0, nu=1, apart from logarithmic corrections. We also show by examples that, in higher dimensions, such transitions may either become continuous or remain first order in the presence of randomness.