0 60 30 01 v 1 2 8 Fe b 20 06 Theoretical and computational aspects of 1 - vertex transfer matrices

نویسنده

  • K. Markström
چکیده

We introduce the notion of 1-vertex transfer matrix for near neighbor Potts models with k kinds of particles. We show that the topological entropy (free energy) of this model can be expressed as the limit the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix that is used. We apply our methods to find the first 15 digits of the entropy of the hard core model on the two dimensional integer grid. 2000 Mathematics Subject 2000 Mathematics Subject Classification: 05A16, 28D20, 37M25, 82B20

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تاریخ انتشار 2006