Quenched random mass disorder in the large N theory of vector bosons

TL;DR

This paper investigates the effects of quenched random mass disorder in the large N limit of the bosonic O(N) vector model, revealing scale-invariant behaviors and fixed points relevant to experimental systems.

Contribution

It provides an exact solution at infinite N, explores fixed points at various dimensions, and predicts critical exponents for future numerical and experimental validation.

Findings

Exact solution at N=∞ reveals two scale-invariant theories.

Disordered fixed point persists at d=2+ε dimensions.

No stable fixed point found below four dimensions, but some fixed points survive at d=3.

Abstract

We study the critical bosonic O(N) vector model with quenched random mass disorder in the large N limit. Due to the replicated action which is sometimes not bounded from below, we avoid the replica trick and adopt a traditional approach to directly compute the disorder averaged physical observables. At $N=\infty$, we can exactly solve the disordered model. The resulting low energy behavior can be described by two scale invariant theories, one of which has an intrinsic scale. At finite $N$, we find that the previously proposed attractive disordered fixed point at $d=2$ continues to exist at $d=2+\epsilon$ spatial dimensions. We also studied the system in the $3<d<4$ spatial dimensions where the disorder is relevant at the Gaussian fixed point. However, no physical attractive fixed point is found right below four spatial dimensions. Nevertheless, the stable fixed point at $2+\epsilon$ dimensions can still survive at $d=3$ where the system has experimental realizations. Some critical exponents are predicted in order to be checked by future numerics and experiments.