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

Journal Article · Tue Jan 01 00:00:00 EST 2013 · IEEE Transactions on Magnetics

DOI:https://doi.org/10.1109/TMAG.2013.2250933· OSTI ID:1091662

Eisenbach, Markus ^[1]; Brown, Greg ^[1]; Rusanu, Aurelian ^[1]; Odbadrakh, Khorgolkhuu ^[1]; Nicholson, Don M ^[1]; McCarthy, Carrie V. ^[2]

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1. ORNL
2. University of Georgia, Athens, GA

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).

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1091662
• Journal Information: IEEE Transactions on Magnetics, Vol. 49, Issue 7; ISSN 0018--9464
• Country of Publication: United States
• Language: English