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The Ising partition function for 2D grids with periodic boundary: Computation and analysis
KTH, Superseded Departments, Physics.
2002 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 108, no 04-mar, 429-457 p.Article in journal (Refereed) Published
Abstract [en]

The Ising partition function for a graph counts the number of bipartitions of the vertices with given sizes, with a given size of the induced edge cut. Expressed as a 2-variable generating function it is easily translatable into the corresponding partition function studied in statistical physics. In the current paper a comparatively efficient transfer matrix method is described for computing the generating function for the nxn grid with periodic boundary. We have applied the method to up to the 15 x 15 grid, in total 225 vertices. We examine the phase transition that takes place when the edge cut reaches a certain critical size. From the physical partition function we extract quantities such as magnetisation and susceptibility and study their asymptotic behaviour at the critical temperature.

Place, publisher, year, edition, pages
2002. Vol. 108, no 04-mar, 429-457 p.
Keyword [en]
2D Ising model, partition function, external non-zero field, exact computation, transfer matrix, model
URN: urn:nbn:se:kth:diva-21592ISI: 000175974300003OAI: diva2:340290
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Lundow, Per Håkan
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