Phase transitions in the generalized XY model at f=1/2

We numerically investigate the phase transitions in the generalized XY model at the frustration f = 1/2, in which the cosine interaction term in the original XY model is extended to the form V (P) (0) = Ei (2 /P2)[1 _ CoS2P2 (0/2)] with the gauge-invariant phase difference 0 and the coupling strength Ei. As either the temperature T or the parameter p in the interaction potential is decreased, the Z2 symmetry related with the two degenerate ground states of the original fullyfrustrated XY model, corresponding to p = 1, is spontaneously broken at TZ2. The quasi-long-range order related with the U(1) symmetry is detected from the helicity modulus, from which the transition temperature TU (1) is determined. The phase diagram in the (T, p) plane with phase boundaries for Tz, and TU(1) is constructed via Monte-Carlo calculations. As p is increased at low temperatures, a nonmonotonic behavior of the helicity modulus with a cusp-like structure is revealed when the ground state changes at p. = V/1'n(3/4)/ ln(cos(7r/8))/2 z 1.3479.