Restoration of Isotropy in the Ising Model on the Sierpinski Gasket

TL;DR

This paper investigates how anisotropic interactions in the Ising model on the Sierpinski gasket become isotropic at low temperatures, revealing conditions for partial or complete restoration of isotropy through renormalization group analysis.

Contribution

It demonstrates that anisotropic spin interactions in the Ising model on a fractal lattice tend to restore isotropy at low temperatures, providing a detailed analysis of the conditions and behavior.

Findings

Correlation lengths become isotropic as temperature approaches zero.

Restoration of isotropy can be partial or complete depending on interactions.

Leading-order singular behavior of correlation lengths is characterized.

Abstract

We study the ferromagnetic Ising model on the Sierpinski gasket (SG), where the spin-spin interactions depends on the direction. Using the renormalization group method, we show that the ratios of the correlation lengths restore the isotropy of the lattice as the temperature approaches zero. This restoration is either partial or perfect, depending on the interactions. In case of partial restoration, we also evaluate the leading-order singular behavior of the correlation lengths.