Potts models on hierarchical lattices and Renormalization Group dynamics II: examples and numerical results

TL;DR

This paper derives exact renormalization maps and analyzes Lee-Yang and Fisher zeros for Potts models on various hierarchical lattices, providing detailed numerical results and examples within a broader theoretical framework.

Contribution

It introduces exact renormalization maps and zero distributions for Potts models on multiple hierarchical lattices, expanding the understanding of these models in complex structures.

Findings

Exact renormalization maps for different lattices

Distribution plots of Lee-Yang and Fisher zeros

Numerical results illustrating phase transition behavior

Abstract

We obtain the exact renormalization map and plots of Lee-Yang and Fisher zeros distributions for Potts models on a number of hierarchical lattices: the diamond hierarchical lattice, a lattice we call spider web, the Sierpinski gasket and cylinders. Such models are only examples among the ones we can study in the general framework of hierarchical lattices, developed in a previous paper.