Numerical investigation of the ageing of the fully frustratedXY model

Abstract

We study the out-of-equilibrium dynamics of the fully frustratedXY model. At equilibrium, this model undergoes two phase transitions at two very closetemperatures: a Kosterlitz–Thouless topological transition and a second-order phasetransition between a paramagnetic phase and a low-temperature phase where thechiralities of the lattice plaquettes are antiferromagnetically ordered. We computeby means of Monte Carlo simulations two-time spin–spin and chirality–chiralityautocorrelation and response functions. From the dynamics of the spin wavesin the low-temperature phase, we extract the temperature-dependent exponentη. We provide evidence for logarithmic corrections above the Kosterlitz–Thouless temperatureand interpret them as a manifestation of free topological defects. Our estimates of theautocorrelation exponent and the fluctuation-dissipation ratio differ from theXY values,while η(TKT) lies at the boundary of the error bar. Indications for logarithmic corrections at thesecond-order critical temperature are presented. However, the coupling betweenangles and chiralities is still strong and explains why the autocorrelation exponentand fluctuation-dissipation ratio are far from the Ising values and seem stable.