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

by Han Ma

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Submission summary

Authors (as registered SciPost users): Han Ma
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-12-01
Date submitted: 2022-11-21 16:26
Submitted by: Ma, Han
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


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.

List of changes

1.We have added the explanation of "generalized free field" as a footnote on p.g.12.
2. We have added a brief analysis of dimension reduction for the d=3 system at the end of IV B on p.g. 17.

Published as SciPost Phys. 14, 039 (2023)

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