Thermal excitations of frustrated XY spins in two dimensions

We present a variational approach to the study of phase transitions in frustrated two-dimensional XY models. In the spirit of Villain's approach for the ferromagnetic case we divide thermal excitations into a low-temperature long-wavelength part (LW) and a high-temperature short-wavelength (SW) part. In the present work we mainly deal with LW excitations and we explicitly consider the cases of the fully frustrated triangular (FFT) and square (FFSQ) XY models. An aspect of our method is that it preserves the coupling between phase (spin angles) and chiral degrees of freedom. LW fluctuations consist of coupled phase and chiral excitations. As a result, we find that for frustrated systems the effective interactions between phase variables is long range and oscillatory in contrast to the unfrustrated problem. Using Monte Carlo simulations we show that our analytical calculations produce accurate results at all temperature T; this is seen at low T in the spin-wave stiffness constant: and in the staggered chirality; this is also the case near T-c: Transitions are driven by the SW part associated with domain walls and vortices, but the coupling between phase and chiral variables is still relevant in the critical region. In that regime our analytical results yield the correct T dependence for bare couplings (given by the LW fluctuations) such as the Coulomb gas temperature T-CG of the frustrated XY models. In particular we find that T-CG tracks chiral rather than phase fluctuations. Our results provide support for a single phase transition scenario in the FFT XY and FFSQ XY models.