Exact Enumeration of the Phase Space of an Ising Model of Ni$_{2}$ MnGa

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 'sing 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 physics of the system. Here we present an 'sing model for the magnetic sublattices of the important magneto-caloric material Ni
₂
MnGa and use an exact enumeration algorithm to calculate the number of states for each energy and sublattice magnetizations M
_Ni
and M
_Mn
. 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 to 48 sites, which provides important insight into the mechanism for the large magnet-caloric effect in Ni
₂
MnGa as well as an important benchmark for Monte-Carlo (esp. Wang-Landau method).