Restoration of Isotropy for Spin Models

TL;DR

This paper investigates how anisotropic spin models on fractal lattices tend to become isotropic at larger scales, using real-space renormalisation to quantify the decay of anisotropy.

Contribution

It introduces a decimation method on fractal lattices to explicitly compute anisotropy decay coefficients, demonstrating universality in lattice field theories on fractals.

Findings

Anisotropy decays exponentially near the isotropic point.

Restoration of isotropy occurs on macroscopic scales.

Results suggest universality across different spin systems.

Abstract

Using real-space renormalisation techniques we analyse the Ising model on a Sierpi\'nski gasket with anisotropic microscopic couplings, and observe a restoration of isotropy on macroscopic scales. In particular, via use of a decimation procedure directly on the fractal lattice, we calculate explicitly the exponential anisotropy decay coefficients near the isotropic regime for both ferromagnetic and antiferromagnetic systems. The results suggest the universality of the phenomenon in lattice field theories on fractals.