SciPost Phys. 14, 039 (2023) ·
published 17 March 2023
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
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.
SciPost Phys. 12, 046 (2022) ·
published 1 February 2022
The $\beta$-functions describe how couplings run under the renormalization
group flow in field theories. In general, all couplings that respect the
symmetry and locality are generated under the renormalization group flow, and
the exact renormalization group flow is characterized by the $\beta$-functions
defined in the infinite dimensional space of couplings. In this paper, we show
that the renormalization group flow is highly constrained so that the
$\beta$-functions defined in a measure zero subspace of couplings completely
determine the $\beta$-functions in the entire space of couplings. We provide a
quantum renormalization group-based algorithm for reconstructing the full
$\beta$-functions from the $\beta$-functions defined in the subspace. As
examples, we derive the full $\beta$-functions for the $O(N)$ vector model and
the $O_L(N) \times O_R(N)$ matrix model entirely from the $\beta$-functions
defined in the subspace of single-trace couplings.
Submissions for which this Contributor is identified as an author:
Dr Ma: "We thank the referee for revie..."
in Submissions | report on Quenched random mass disorder in the large N theory of vector bosons