Temperature-disorder phase diagram of a three-dimensional gauge-glass model

Vincenzo Alba and Ettore Vicari
Phys. Rev. B 83, 094203 – Published 25 March 2011

Abstract

We investigate the temperature-disorder (T-σ) phase diagram of a three-dimensional gauge glass model, which is a cubic-lattice nearest-neighbor XY model with quenched random phase shifts Axy at the bonds. We consider the uncorrelated phase-shift distribution P(Axy)~exp[(cosAxy)/σ], which has the pure XY model, and the uniform distribution of random phase shifts as extreme cases at σ=0 and σ, respectively, and which gives rise to equal magnetic and overlap correlation functions when T=σ. Our study is mostly based on numerical Monte Carlo simulations. While the high-temperature phase is always paramagnetic, at low temperatures there is a ferromagnetic phase for weak disorder (small σ) and a glassy phase at large disorder (large σ). These three phases are separated by transition lines with different magnetic and glassy critical behaviors. The disorder induced by the random phase shifts turns out to be irrelevant at the paramagnetic-ferromagnetic transition line, where the critical behavior belongs to the 3D XY universality class of pure systems; disorder gives rise only to very slowly decaying scaling corrections. The glassy critical behavior along the paramagnetic-glassy transition line belongs to the gauge-glass universality class, with a quite large exponent ν=3.2(4). These transition lines meet at a multicritical point M, located at TM=σM=0.7840(2). The low-temperature ferromagnetic and glassy phases are separated by a third transition line, from M down to the T=0 axis, which is slightly reentrant.

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  • Received 15 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.094203

©2011 American Physical Society

Authors & Affiliations

Vincenzo Alba*

  • Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany Scuola Normale Superiore and INFN, I-56126 Pisa, Italy

Ettore Vicari

  • Dipartimento di Fisica dell’Università di Pisa and INFN, I-56127 Pisa, Italy

  • *vincenzo@pks.mpg.de
  • ettore.vicari@df.unipi.it

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Vol. 83, Iss. 9 — 1 March 2011

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