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

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).

Authors:
 [1];  [1];  [1];  [1];  [1];  [2]
  1. ORNL
  2. University of Georgia, Athens, GA
Publication Date:
Research Org.:
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 Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1091662
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Journal Article
Journal Name:
IEEE Transactions on Magnetics
Additional Journal Information:
Journal Volume: 49; Journal Issue: 7; Journal ID: ISSN 0018--9464
Country of Publication:
United States
Language:
English

Citation Formats

Eisenbach, Markus, Brown, Greg, Rusanu, Aurelian, Odbadrakh, Khorgolkhuu, Nicholson, Don M, and McCarthy, Carrie V. Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa. United States: N. p., 2013. Web. doi:10.1109/TMAG.2013.2250933.
Eisenbach, Markus, Brown, Greg, Rusanu, Aurelian, Odbadrakh, Khorgolkhuu, Nicholson, Don M, & McCarthy, Carrie V. Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa. United States. https://doi.org/10.1109/TMAG.2013.2250933
Eisenbach, Markus, Brown, Greg, Rusanu, Aurelian, Odbadrakh, Khorgolkhuu, Nicholson, Don M, and McCarthy, Carrie V. 2013. "Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa". United States. https://doi.org/10.1109/TMAG.2013.2250933.
@article{osti_1091662,
title = {Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa},
author = {Eisenbach, Markus and Brown, Greg and Rusanu, Aurelian and Odbadrakh, Khorgolkhuu and Nicholson, Don M and McCarthy, Carrie V.},
abstractNote = {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).},
doi = {10.1109/TMAG.2013.2250933},
url = {https://www.osti.gov/biblio/1091662}, journal = {IEEE Transactions on Magnetics},
issn = {0018--9464},
number = 7,
volume = 49,
place = {United States},
year = {Tue Jan 01 00:00:00 EST 2013},
month = {Tue Jan 01 00:00:00 EST 2013}
}