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Specific heat and energy for the three-dimensional O(2) model

We investigate the three-dimensional O(2) model on lattices of size 8^3 to 160^3 close to the critical point at zero magnetic field. We confirm explicitly the value of the critical coupling J_c found by Ballesteros et al. and estimate there the universal values of g_r and xi/L. At the critical point we study the finite size dependencies of the energy density epsilon and the specific heat C. We find that the nonsingular part of the specific heat C_{ns} is linearly dependent on 1/alpha. From the critical behaviour of the specific heat for T not T_c on the largest lattices we determine the universal amplitude ratio A+/A-. The alpha- dependence of this ratio is close to the phenomenological relation A+/A- = 1-4alpha.