Another solution of 2D Ising model

  • S. N. VergelesEmail author
Statistical, Nonlinear, and Soft Matter Physics


The partition function of the Ising model on a two-dimensional regular lattice is calculated by using the matrix representation of a Clifford algebra (the Dirac algebra), with number of generators equal to the number of lattice sites. It is shown that the partition function over all loops in a 2D lattice including self-intersecting ones is the trace of a polynomial in terms of Dirac matrices. The polynomial is an element of the rotation group in the spinor representation. Thus, the partition function is a function of a character on an orthogonal group of a high degree in the spinor representation.

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia

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