  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 |T-T_c|/T_c \approx 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 beta_c and data for the internal energy
and the specific heat at \beta_c recently obtained in cond-mat/0605083. We find
R_{\alpha} = (1-A_+/A_-)/\alpha = 4.01(5), where alpha is the critical exponent
of the specific heat and A_{\pm} is the amplitude of the specific heat in the
high and the low temperature phase, respectively.
