Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa

• Published in: IEEE transactions on magnetics 2013-07, Vol.49 (7), p.3141-3143
• Main Authors: EISENBACH, Markus, BROWN, Gregory, MCCARTY, Carrie V, RUSANU, Aurelian, ODBADRAKH, Khorgolkhuu, NICHOLSON, Don M
• Format: Article
• Language: English
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Materials science; Other topics in materials science; Physics
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2013.2250933

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).