Fractal structure of the six-vertex model
نویسنده
چکیده
A fractal set which corresponds to the six-vertex model has been obtained and a relationship between the free energy of the six-vertex model and the fractal dimension of the fractal set was established. Notions which correspond to the transfer matrix and the n-equivalence has been found in the area of the fractal geometry. This correspondence can be generalized to the case of the models suitable to the transfer matrix treatment.
منابع مشابه
Transmission properties of one dimensional fractal structures
In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...
متن کاملFractal structure of a solvable lattice model
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 b...
متن کاملApplication of spectrum-volume fractal modeling for detection of mineralized zones
The main goal of this research work was to detect the different Cu mineralized zones in the Sungun porphyry deposit in NW Iran using the Spectrum-Volume (S-V) fractal modeling based on the sub-surface data for this deposit. This operation was carried out on an estimated Cu block model based on a Fast Fourier Transformation (FFT) using the C++ and MATLAB programing. The S-V log-log plot was gene...
متن کاملExact Solution of the Six-Vertex Model on a Random Lattice
We solve exactly the 6-vertex model on a dynamical random lattice, using its representation as a large N matrix model. The model describes a gas of dense nonintersecting oriented loops coupled to the local curvature defects on the lattice. The model can be mapped to the c = 1 string theory, compactified at some length depending on the vertex coupling. We give explicit expression for the disk am...
متن کاملGeneralized boundary condition , free energies of six - vertex models and fractal dimension
The structures of the configuration space of the six-vertex models with various boundaries and boundary conditions are investigated, and it is derived that the free energies depend on the boundary conditions, and that they are classified by the fractal structures. The ”n-equivalences” of the boundary conditions are defined with a property that the models with nequivalent boundary conditions res...
متن کامل