Asymptotic formulas for integer partitions within the approach of   microcanonical ensemble
  The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary (one-dimensional) partitions, the correction to the leading asymptotic is obtained. The estimate for the number of two-dimensional (plane) partitions coincides with known asymptotic results. 
D. Prokhorov, A. Rovenchak
cond-mat.stat-mech