Critical behavior of the planar magnet model in three dimensions

Details Critical behavior of the planar magnet model in three dimensions Critical behavior of the planar magnet model in three dimensions

1998-11-18

arxiv.org/abs/cond-mat/9811276v1

Physics

Condensed Matter

Statistical Mechanics

11 pages, 5 figures

Scientific paper

10.1103/PhysRevB.59.11575

We use a hybrid Monte Carlo algorithm in which a single-cluster update is combined with the over-relaxation and Metropolis spin re-orientation algorithm. Periodic boundary conditions were applied in all directions. We have calculated the fourth-order cumulant in finite size lattices using the single-histogram re-weighting method. Using finite-size scaling theory, we obtained the critical temperature which is very different from that of the usual XY model. At the critical temperature, we calculated the susceptibility and the magnetization on lattices of size up to $42^3$. Using finite-size scaling theory we accurately determine the critical exponents of the model and find that $\nu$=0.670(7), $\gamma/\nu$=1.9696(37), and $\beta/\nu$=0.515(2). Thus, we conclude that the model belongs to the same universality class with the XY model, as expected.

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