The three-dimensional XY universality class:: a high precision Monte Carlo estimate of the universal amplitude ratio A+/A-

We simulate the improved three-dimensional two-component phi(4) model on the simple cubic lattice in the low and the high temperature phase for reduced temperatures down to vertical bar T-T-c vertical bar/T-c approximate to 0.0017 on lattices of size up to 350(3). Our new results for the internal energy and the specific heat are combined with the accurate estimates of beta(c) and data for the internal energy and the specific heat at beta(c) recently obtained in Campostrini et al (2006 Preprint cond-mat/0605083). We find R-alpha = (1-A(+)/A(-))/alpha = 4.01(5), where a is the critical exponent of the specific heat and A(+/-) is the amplitude of the specific heat in the high and the low temperature phase, respectively.