Thermodynamics of ultra-small metallic grains in the auxiliary-field Monte Carlo approach

We use an auxiliary-field Monte Carlo (AFMC) method to calculate thermodynamic properties (spin susceptibility and heat capacity) of ultra-small metallic grains in the presence of pairing correlations. This method allows us to study the crossover from bulk systems, where mean-field BCS theory is valid, to the fluctuation-dominated regime of ultra-small particles at finite temperature. The computational effort at low temperatures is significantly reduced by exploiting a simple renormalization method.