Gravity/Spin-model correspondence and holographic superfluids

TL;DR

This paper establishes a correspondence between gravity models and spin systems, revealing insights into phase transitions and critical behavior in holographic superfluids through a gravity-spin analogy.

Contribution

It introduces a novel gravity-spin model correspondence and analyzes phase transitions using a linear-dilaton CFT in a holographic superfluid context.

Findings

Near the phase transition, observables follow mean-field scaling.

Black-hole phases correspond to ordered phases, graviton gases to disordered phases.

The second speed of sound vanishes at the transition with mean-field exponent.

Abstract

We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in ferromagnets. The black-hole phase corresponds to the ordered and the graviton gas corresponds to the disordered phases respectively. A simple set-up based on Einstein-dilaton gravity indicates that the vicinity of the phase transition is governed by a linear-dilaton CFT. Employing this CFT we calculate scaling of observables near T_c, and obtain mean-field scaling in a semi-classical approximation. In case of the XY model the Goldstone mode is identified with the zero mode of the NS-NS two-form. We show that the second speed of sound vanishes at the transition also with the mean field exponent.