Fractal structure of a solvable lattice model

Details Fractal structure of a solvable lattice model Fractal structure of a solvable lattice model

2007-12-31

arxiv.org/abs/0801.0186v2

Physics

Condensed Matter

Statistical Mechanics

14 pages and a figure

Scientific paper

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.

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