IJPAM: Volume 59, No. 3 (2010)

FRACTAL STRUCTURE OF A SOLVABLE LATTICE MODEL

Kazuhiko Minami
Graduate School of Mathematics
Nagoya University
Chikusa-ku, Nagoya, 464-8602, JAPAN
e-mail: minami@math.nagoya-u.ac.jp


Abstract.Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer matrix method and the $n$-equivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can be generalized for the models suitable to the transfer matrix treatment, and hence this gives general relation between solvable lattice models and fractal geometry.

Received: November 25, 2009

AMS Subject Classification: 28A80, 82B20, 82B23

Key Words and Phrases: IFS fractal, six-vertex model, solvable lattice models, transfer matrix, $n$-equivalence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 3