Kink-antikink unbinding transition in the two-dimensional fully frustrated XY model

The two-dimensional s2Dd fully frustrated XY sFFXYd model 1,2 is one of the most intriguing of the “simple” statistical mechanics models. The doubly degenerate checkerboard pattern of vortices in the ground state leads to an Isinglike discrete Zs2d symmetry in addition to the KosterlitzThouless-like continuous Os2d symmetry associated with the uniform rotation of all phase angles.3 It remains controversial whether there are two distinct phase transitions TKT,TI, with TKT marking the breaking of the Os2d symmetry and TI marking the breaking of the Zs2d symmetry,4–6 or, rather, a single transition in which both symmetries are broken simultaneously.7 Recently, Korshunov8 presented an argument for a new interfacial transition Tw in the 2D FFXY model, lying well below the bulk transitionssd, arising from the unbinding of step excitations of unit height s“kink-antikink pairs”d on the domain walls associated with the Zs2d symmetry. Korshunov argued that the kink-antikink unbinding transition leads to a decoupling of phase coherence across domain boundaries, supporting the identification of the FFXY with the coupled XY-Ising model.9 Korshunov further argued that this effect necessarily leads to the scenario of two distinct bulk transitions, TKT,TI. Earlier, Lee and co-workers, first in simulations of the 2D FFXY model with Langevin dynamics,10 and then in its dual Coulomb gas sCGd model with Monte Carlo sMCd dynamics,11 found evidence for a transition in domain wall morphology in simulations of the ordering kinetics of domain growth following a sudden quench. They interpreted this as a finite-temperature roughening transition of the Ising-like domain walls. Jeon et al.12 made similar conclusions in simulations of the 2D FFXY with resistively shunted junction dynamics. Korshunov,8 however, has argued that domain walls should be rough at all temperatures. In this paper we present direct numerical evidence demonstrating the existence of the kink-antikink unbinding transition at a temperature Tw below the bulk transitionssd. In agreement with Korshunov’s predictions, we show that phase angles on opposite sides of the domain wall decouple above Tw. The numerical value we find for Tw is comparable to that of the morphological transition found by Lee et al.,11 however, we explicitly demonstrate that the domain walls are rough at temperatures well below Tw. This indicates that the transition seen by Lee and co-workers was really kinkantikink unbinding, rather than roughening. II. THE MODEL