Abstract
Exact evaluations of partition functions are generally prohibitively expensive due to exponential growth of phase space with the number of degrees of freedom. For an Ising model with  sites the number of possible states is   requiring the use of better scaling methods such as importance sampling Monte-Carlo calculations for all but the smallest systems. Yet the ability to obtain exact solutions for as large as possible systems can provide important benchmark results and opportunities for unobscured insight into the underlying physicsofthesystem.HerewepresentanIsingmodelforthemagneticsublatticesoftheimportantmagneto-caloricmaterialNi MnGa and use an exact enumeration algorithm to calculate the number of states             for each energy  and sublattice magne- tizations    and    . This allows the efficient calculation of the partition function and derived thermodynamic quantities such as specific heat and susceptibility. Utilizing the jaguarpf system at Oak Ridge we are able to calculate             for systems of up to48sites,whichprovidesimportantinsightintothemechanismforthelargemagnet-caloriceffectinNi MnGaaswellasanimportant benchmark for Monte-Carlo (esp. Wang-Landau method).
