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Extinction of BKT transition by nonmagnetic disorder in planar-symmetry spin models

G. M. Wysin·A. R. Pereira·I. A. Marques·S. A. Leonel·P. Z. Coura
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Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional planar rotator and XY models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster and over-relaxation techniques. The transition temperature $T_c$ is determined as a function of vacancy density $ρ_{vac}$ by calculations of the helicity modulus and the by finite-size scaling of the in-plane magnetic susceptibility. The results for $T_c$ are consistent with those from the much less precise fourth-order cumulant of Binder. $T_c$ is found to decrease monotonically with increasing $ρ_{vac}$, and falls to zero close to the square lattice percolation limit, $ρ_{vac}\approx 0.41$ . The result is physically reasonable: the long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.

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G. M. Wysin, A. R. Pereira, I. A. Marques, S. A. Leonel, P. Z. Coura. 2005-04-06. Extinction of BKT transition by nonmagnetic disorder in planar-symmetry spin models. https://arxiv.org/abs/cond-mat/0504145

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