Numerical investigation of the aging of the Fully-Frustrated XY model

Abstract

We study the out-of-equilibrium dynamics of the fully-frustrated XY model. At equilibrium, this model undergoes two phase transitions at two very close temperatures: a Kosterlitz-Thouless topological transition and a second-order phase transition between a paramagnetic phase and a low-temperature phase where the chiralities of the lattice plaquettes are anti-ferromagnetically ordered. We compute by Monte Carlo simulations two-time spin-spin and chirality-chirality autocorrelation and response functions. From the dynamics of the spin waves in the low temperature phase, we extract the temperature-dependent exponent $\eta$. We provide evidences for logarithmic corrections above the Kosterlitz-Thouless temperature and interpret them as a manifestation of free topological defects. Our estimates of the autocorrelation exponent and the fluctuation-dissipation ratio differ from the XY values, while $\eta(T_{\rm KT})$ lies at the boundary of the error bar. Indications for logarithmic corrections at the second-order critical temperature are presented. However, the coupling between angles and chiralities is still strong and explains why autocorrelation exponent and fluctuation-dissipation ratio are far from the Ising values and seems stable.