NEW ALGORITHM FOR THE COMPUTATION OF THE PARTITION FUNCTION FOR THE ISING MODEL ON A SQUARE LATTICE

K. Malarz (), M. S. Magdoń-Maksymowicz (), A. Z. Maksymowicz (), B. Kawecka-Magiera () and K. Kułakowski ()
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K. Malarz: Department of Applied Computer Science, Faculty of Physics and Nuclear, Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
M. S. Magdoń-Maksymowicz: Department of Mathematical Statistics, Agriculture University, al. Mickiewicza 21, PL-31120 Kraków, Poland
A. Z. Maksymowicz: Department of Applied Computer Science, Faculty of Physics and Nuclear, Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
B. Kawecka-Magiera: Department of Applied Computer Science, Faculty of Physics and Nuclear, Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland
K. Kułakowski: Department of Applied Computer Science, Faculty of Physics and Nuclear, Techniques, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 05, 689-694

Abstract: A new and efficient algorithm is presented for the calculation of the partition function in theS=±1Ising model. As an example, we use the algorithm to obtain the thermal-dependence of the magnetic spin susceptibility of an Ising antiferromagnet for a 8×8 square lattice with open boundary conditions. The results agree qualitatively with the prediction of the Monte Carlo simulations and the experimental data, and they are better than the mean field approach results. For the 8×8 lattice, the algorithm reduces the computation time by nine orders of magnitude.

Keywords: Antiferromagnets; Ising model; magnetic susceptibility; mean field approximation; world records (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S012918310300484X

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