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Journal of Statistical Physics

, Volume 77, Issue 1–2, pp 77–87 | Cite as

A goldstone mode in the Kawasaki-Ising model

  • Claudio Albanese
Articles

Abstract

The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a “quantum” extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.

Key Words

Ising model Monte Carlo dynamics spontaneous gauge symmetry breaking 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Claudio Albanese
    • 1
  1. 1.Institute for Advanced StudySchool of MathematicsPrinceton

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