Communications in Theoretical Physics

Phase Transition and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice

Ke Jin, Chen Tian-Lun, Wu-Qun Huang

Published Jul 1, 1989• 0 citations

Abstract

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility shows a clear size-dependent low temperature region. This means that it should be divergent in this region.

DOI: 10.1088/0253-6102/12/1/99

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Communications in Theoretical Physics

Phase Transition and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice

Ke Jin, Chen Tian-Lun, Wu-Qun Huang

Published Jul 1, 1989• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/12/1/99

Related papers

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Journal of Physics A Mathematical and GeneralOct 7, 19892 citations

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Tian Wang, T. L. Chen

Communications in Theoretical PhysicsMar 1, 19930 citations

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We present detailed Monte Carlo results for the susceptibility \ensuremath{\chi}, correlation length \ensuremath{\xi}, and specific heat

{\mathit{C}}_{\mathit{v}}

for the XY model. The simulations are done on

{64}^{2}

{128}^{2}

{256}^{2}

, and

{512}^{2}

lattices over the temperature range 0.98\ensuremath{\le}T\ensuremath{\le}1.43 corresponding to 270. Fits to \ensuremath{\chi} and \ensuremath{\xi} data favor a Kosterlitz-Thouless (KT) singularity over a second-order transition; however, unconstrained four-parameter KT fits do not confirm the predicted values \ensuremath{\nu}=0.5 and \ensuremath{\eta}=0.25. Our best estimate,

{\mathit{T}}_{\mathit{c}}

=0.894(5), is obtained using KT fits with \ensuremath{\nu} fixed at 0.5. The exponent \ensuremath{\eta} is calculated as a function of temperature in the spin-wave phase using Monte Carlo renormalization-group and finite-size-scaling methods. Both methods give consistent results and we find \ensuremath{\eta}\ensuremath{\approxeq}0.235 at T=0.894. We also present results for the behavior of vortex density across the transition and exhibit how the dilute-gas approximation breaks down.

We study the two-dimensional generalized XY model that depends on an integer

q

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

q

, 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

q

without assuming a specific universal form in terms of the KT transition temperature

T_{\rm KT}

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.