Exact enumeration of the phase space of an Ising model of Ni 2MnGa

Markus Eisenbach, Gregory Brown, Carrie V. Mccarty, Aurelian Rusanu, Khorgolkhuu Odbadrakh, Don M. Nicholson

Research output: Contribution to journalArticlepeer-review

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 N sites the number of possible states is 2N 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 Ising model for the magnetic sublattices of the important magneto-caloric material Ni2 MnGa and use an exact enumeration algorithm to calculate the number of states g(E,MNi,MMn) for each energy E and sublattice magnetizations MNi and MMn. 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 g(E,MNi,MMn) for systems of up to 48 sites, which provides important insight into the mechanism for the large magnet-caloric effect in Ni2MnGa as well as an important benchmark for Monte-Carlo (esp. Wang-Landau method).

Original languageEnglish
Article number6558899
Pages (from-to)3141-3143
Number of pages3
JournalIEEE Transactions on Magnetics
Volume49
Issue number7
DOIs
StatePublished - 2013
Externally publishedYes

Keywords

  • Exact results
  • Ising Model
  • Magneto caloric materials
  • Statistical physics

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