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Physical review. B, Condensed matter

Phase diagram of the anisotropic XY model

Yu‐qiang Ma, W. Figueiredo

Published Mar 1, 1997• 22 citations
Publisher

Abstract

The quantum version of the XY model in the presence of anisotropy is presented in the boson space and solved exactly in the spherical limit. We obtain the temperature (T) - anisotropy (D) phase diagram of the model for the dimension d>${\mathrm{d}}_{\mathrm{c}}$=2, where ${\mathrm{d}}_{\mathrm{c}}$ is the lower critical dimension. It is shown that the critical temperature ${\mathrm{T}}_{\mathrm{c}}$ below which a ferromagnetic phase appears increases with increasing the anisotropy parameter, and remains finite even for anisotropy parameter D\ensuremath{\gg}:1.

DOI
10.1103/physrevb.55.5604

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The quantum version of the random-field spherical XY\mathrm{XY}XY model on a ddd-dimensional hypercubic lattice is presented in the boson space, and solved exactly. We recover the Imry-Ma result concerning the lower critical dimension dc=4,{d}_{c}=4,dc​=4, and calculate the critical exponents near the critical temperature. In particular, we obtain a general phase diagram of the model with arbitrary dimension ddd when d>dc.d>{d}_{c}.d>dc​. The ferromagnetic ordering is reduced by quantum fluctuations, and destroyed completely by random-field fluctuations with sufficiently large values of the random-field variance \ensuremath{\sigma}. The entropy and the specific heat vanish as Td/2{T}^{d/2}Td/2 at low temperatures. Since the model is equivalent to a Bose system, we show a superfluid-Mott insulator transition at a critical chemical potential ${\ensuremath{\mu}}_{c}.$
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