Magnetization and overlap distributions of the ferromagnetic Ising model on the Cayley tree

TL;DR

This paper investigates the behavior of magnetization and overlap distributions in the ferromagnetic Ising model on the Cayley tree, focusing on their asymptotic scaling and fractal properties.

Contribution

It provides new insights into the asymptotic moments and fractal dimensions of magnetization and overlap measures in this specific model.

Findings

Analysis of asymptotic scaling of moments

Calculation of fractal dimensions of measures

Characterization of distribution properties

Abstract

We analyze the magnetization and the overlap distributions on the ferromagnetic Cayley tree. Two quantities are investigated: the asymptotic scaling of all the moments of the magnetization and overlap distributions, as well as the computation of the fractal dimension of the magnetization and overlap probability measures.