Generic Ising Trees

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 ${\bar{d}}_s=4/3$.

29 pages, 2 figures; typos corrected, one section and new references added

References in corpus (7)

• Local limit of labeled trees and expected volume growth in a random quadrangulation
• The spectral dimension of generic trees
• On the spectral dimension of causal triangulations
• Condensation in nongeneric trees
• Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations
• Appearance of vertices of infinite order in a model of random trees
• Phase transition for the Ising model on the Critical Lorentzian triangulation

Cited by in corpus (3)

• New multicritical matrix models and multicritical 2d CDT
• The Ising model on the random planar causal triangulation: bounds on the critical line and magnetization properties
• Critical behaviour of loop models on causal triangulations