Se p 20 05 Critical behavior of two - dimensional fully frustrated XY systems

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 × L, L . 10. We show that the lowtemperature 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 KosterlitzThouless 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 νeff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices. 1. Fully frustrated systems In the last few decades there has been a considerable interest in the consequences of frustration on the critical behavior of statistical systems. The simplest example is the antiferromagnetic Ising model on a triangular lattice, whose Hamiltonian is