Spin-chirality decoupling and critical properties of a two-dimensional fully frustrated XY model

We study the ordering of spin and chirality in the fully frustrated XY model on a square lattice by extensive Monte Carlo simulations. In addition to standard quantities, we studied the vorticity modulus introduced by Kawamura and Kikuchi [Phys. Rev. B 47, 1134 (1993)], which has a simple Coulomb-gas representation as we show in the present paper, to obtain further insight into the problem. In accord with recent results by Hasenbusch et al. [Phys. Rev. B 72, 184502 (2005)] our results indicate unambiguously that spin and chirality exhibit separate phase transitions at two distinct temperatures, i.e., the occurrence of spin-chirality decoupling. The chirality exhibits a long-range order at T-c = 0.453 24(1) via a second-order phase transition, where the spin remains disordered with a finite correlation length xi(s)(T-c) similar to 120. The critical properties of the chiral transition determined from a finite-size scaling analysis for large enough systems of linear size L > xi(s)(T-c) are well compatible with the Ising universality. On the other hand, the spin exhibits a phase transition into a quasi-long-range-ordered phase at a lower temperature, which we estimate to be T-s = 0.442(2), about 0.9% below that found by Hasenbusch et al. On this basis we conclude that eta(T-s) = 0.20(1) which, combined with a study of the specific heat, raises the possibility that the character of the associated higher-order transition differs from that of the conventional Kosterlitz-Thouless transition.