Critical behavior of two-dimensional fully frustrated XY systems

Details Critical behavior of two-dimensional fully frustrated XY systems Critical behavior of two-dimensional fully frustrated XY systems

2005-09-20

arxiv.org/abs/cond-mat/0509511v1

J.Phys.Conf.Ser.42:124-137,2006

Physics

Condensed Matter

Statistical Mechanics

15 pages, Presented at the Conference "Counting Complexity", July 10-15, 2005, Dunk Island, Australia

Scientific paper

10.1088/1742-6596/42/1/013

We study the phase diagram of the two-dimensional fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present Monte Carlo simulations on square lattices $L\times L$, $L\lesssim 10^3$. We show that the low-temperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent $\nu_{\rm eff} \approx 0.8$. This explains the result $\nu\approx 0.8$ of many previous studies using smaller lattices.

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