Gravity/Spin-model correspondence and holographic superfluids

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.

68 pages + appendices, 4 figures; v2: the published version - discussion in section 2 extended, typos corrected, new referenced added

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• Strange Metallic Behaviour and the Thermodynamics of Charged Dilatonic Black Holes
• Thermodynamics and transport of holographic nodal line semimetals
• Quasi-normal modes of a strongly coupled non-conformal plasma and approach to criticality
• Fluctuations in non-conformal holographic plasma at criticality
• Stringy Stability of Charged Dilaton Black Holes with Flat Event Horizon
• Analytic long-lived modes in charged critical plasma
• An analytic approach for holographic entanglement entropy at (quantum) criticality