Computation of the Ising partition function for two-dimensional square grids

Roland Häggkvist, Anders Rosengren, Daniel Andrén, Petras Kundrotas, Per Håkan Lundow, and Klas Markström

Phys. Rev. E 69, 046104 – Published 16 April 2004

Abstract

An improved method for obtaining the Ising partition function of $n \times n$ square grids with periodic boundary is presented. Our method applies results from Galois theory in order to split the computation into smaller parts and at the same time avoid the use of numerics. Using this method we have computed the exact partition function for the $(320 \times 320)$ grid, the $(256 \times 256)$ grid, and the $(160 \times 160)$ grid, as well as for a number of smaller grids. We obtain scaling parameters and compare with what theory prescribes.

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Received 17 October 2003

DOI:https://doi.org/10.1103/PhysRevE.69.046104

Authors & Affiliations

Roland Häggkvist^1,*, Anders Rosengren^2,†, Daniel Andrén^1,‡, Petras Kundrotas^2,§, Per Håkan Lundow^2,∥, and Klas Markström^1,¶

¹Department of Mathematics, Umeå University, SE-901 87 Umeå, Sweden
²Department of Physics, AlbaNova University Center, KTH, SE-106 91 Stockholm, Sweden

^*Electronic address: Roland.Haggkvist@math.umu.se
^†Electronic address: ar@theophys.kth.se
^‡Electronic address: Daniel.Andren@math.umu.se
^§Electronic address: Petras.Kundrotas@csb.ki.se
^∥Electronic address: phl@kth.se
^¶Electronic address: Klas.Markstrom@math.umu.se

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Vol. 69, Iss. 4 — April 2004

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