Heat capacity for systems with excited-state quantum phase transitions
  Heat capacities of model systems with finite numbers of effective degrees of freedom are evaluated using canonical and microcanonical thermodynamics. Discrepancies between both approaches, which are observed even in the infinite-size limit, are particularly large in systems that exhibit an excited-state quantum phase transition. The corresponding irregularity of the spectrum generates a singularity in the microcanonical heat capacity and affects smoothly the canonical heat capacity. 
Pavel Cejnar, Pavel Str\'ansk\'y
quant-ph cond-mat.stat-mech