Algebraic reduction of the Ising model

R. J. Baxter

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)


    We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.

    Original languageEnglish
    Pages (from-to)959-982
    Number of pages24
    JournalJournal of Statistical Physics
    Issue number6
    Publication statusPublished - Sept 2008


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