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arXiv:cond-mat/9703109 · Physical review. B, Condensed matter

Phase transitions in the two-dimensional XY model with random phases: A Monte Carlo study

J. Maucourt, Daniel R. Grempel

Published Aug 1, 1997• 30 citations
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Abstract

We study the two-dimensional $\mathrm{XY}$ model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and temperature. If the strength of the randomness is less than a critical value, ${\ensuremath{\sigma}}_{c},$ the system has a Kosterlitz-Thouless (KT) phase transition from the paramagnetic phase to a state with quasi-long-range order. Our data suggest that the latter exists down to $T=0$ in contradiction with theories that predict the appearance of a low-temperature reentrant phase. At the critical disorder ${T}_{\mathrm{KT}}\ensuremath{\rightarrow}0$ and for $\ensuremath{\sigma}>{\ensuremath{\sigma}}_{c}$ there is no quasiordered phase. At zero temperature there is a phase transition between two different glassy states at ${\ensuremath{\sigma}}_{c}.$ The functional dependence of the correlation length on $\ensuremath{\sigma}$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.

DOI
10.1103/physrevb.56.2572

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We study the two-dimensional generalized XY model that depends on an integer qqq by the Monte Carlo method. This model was recently proposed by Romano and Zagrebnov. We find a single Kosterlitz-Thouless (KT) transition for all values of qqq, in contrast with the previous speculation that there may be two transitions, one a regular KT transition and another a first-order transition at a higher temperature. We show the universality of the KT transitions by comparing the universal finite-size scaling behaviors at different values of qqq without assuming a specific universal form in terms of the KT transition temperature TKTT_{\rm KT}TKT​.
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