Generic Ising Trees

TL;DR

This paper analyzes the Ising model on infinite generic trees, providing a detailed distribution of configurations, studying magnetization properties, and calculating the trees' Hausdorff and spectral dimensions.

Contribution

It introduces a comprehensive description of the Ising model on infinite generic trees and computes key geometric and physical properties.

Findings

No spontaneous magnetization in the system

Hausdorff dimension is 2

Spectral dimension is 4/3

Abstract

The Ising model on an infinite generic tree is defined as a thermodynamic limit of finite systems. A detailed description of the corresponding distribution of infinite spin configurations is given. As an application we study the magnetization properties of such systems and prove that they exhibit no spontaneous magnetization. Furthermore, the values of the Hausdorff and spectral dimensions of the underlying trees are calculated and found to be, respectively, $\bar{d}_h=2$ and $\bar{d}_s=4/3$.