Exchange interaction effects in the thermodynamic properties of quantum   dots
  We study electron-electron interaction effects in the thermodynamic properties of quantum-dot systems. We obtain the direct and exchange contributions to the specific heat C_v in the self-consistent Hartree-Fock approximation at finite temperatures. An exchange-induced phase transition is observed and the transition temperature is shown to be inversely proportional to the size of the system. The exchange contribution to C_v dominates over the direct and kinetic contributions in the intermediate regime of interaction strength (r_s ~ 1). Furthermore, the electron-electron interaction modifies both the amplitude and the period of magnetic field induced oscillations in C_v. 
Luis G. Dias da Silva, Nelson Studart