Thermodynamic functions within the van Hove BCS model: Symmetry mixing effects

All the new layer perovskite superconductors seem to show a phenomenon of symmetry mixing with repect to the order parameter. An analysis of the different alternative of mixing and how far could them be presented is carried out. For the particular case of s+id symmetry of the gap, the temperature dependence of the specific heat ($C_{es}$) and the thermodynamic critical magnetic field ($H_{c}$) are calculated. A double peak transition is observed on $C_{es}(T)$ in the mixed regime while the single peak behavior is recovered for a purely symmetric state (s or d). $C_{es}$ presents a quadratic law at low tempeartures for a d-wave gap and for the s-wave one the typical exponential attenuation. The temperature dependence of $H_{c}$ shows a clear phase transition of second order at temperatures where the d-wave component becomes negligible. A comparison with other results and experiments is done.