Fractal structure of a solvable lattice model

TL;DR

This paper explores the fractal structure of the six-vertex lattice model using IFS, linking fractal dimensions to free energy, and connects lattice theory methods with fractal geometry, suggesting broad applicability.

Contribution

It introduces a novel approach to relate solvable lattice models with fractal geometry through IFS and transfer matrix methods, establishing a general framework.

Findings

Fractal dimension satisfies an equation derived from free energy.

Transfer matrix and $n$-equivalence are applicable in fractal geometry.

Results are generalizable to other models suitable for transfer matrix analysis.

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.