Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model (Communications in Computational Physics, 2008)
Advanced Monte Carlo simulations of magnetisation and susceptibility in3D XY model are performed at two different coupling constants β =0.55 and β =0.5,completing our previous simulation results with additional data points and extendingthe range of the external field to twice as small values as previously reported (h ≥0.00015625). The simulated maximal lattices sizes are also increased from L=384 toL=512. Our aim is an improved estimation of the exponent ρ, describing the Goldstonemode singularity M(h) = M(+0)+chρ at h → 0, where M is the magnetisation. Thedata reveal some unexpected small oscillations. It makes the estimation by many-parameter fits of the magnetisation data unstable, and we are looking for an alternativemethod. Our best estimate ρ = 0.555(17) is extracted from the analysis of effectiveexponents determined from local fits of the susceptibility data. This method givesstable and consistent results for both values of β, taking into account the leading aswell as the subleading correction to scaling. We report also the values of spontaneousmagnetisation.