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 φ 4 model on the simple cubic lattice in the low and the high temperature phase for reduced temperatures down to |T − T c |/T c ≈ 0.0017 on lattices of a size up to 350 3. Our new results for the internal energy and the specific heat are combined with the accurate estimates of β c and data for the internal energy and the specific heat at β c recently obtained in ref. [1]. We find R α = (1 − A + /A −)/α = 4.01(5), where α 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.