Anomalous Behavior of the Zero Field Susceptibility of the Ising Model on the Cayley Tree

TL;DR

This paper investigates the zero field susceptibility of the Ising model on the Cayley tree, revealing an unusual divergence at the critical temperature with a linear relation to the tree level, contrasting typical critical behavior.

Contribution

It uncovers the anomalous divergence behavior of susceptibility on the Cayley tree, showing a linear divergence with tree level and analytic behavior near the critical point.

Findings

Susceptibility diverges proportionally to tree level n at Tc

Behavior of susceptibility is analytic near Tc

Critical exponent gamma=0

Abstract

It is found that the zero field susceptibility chi of the Ising model on the Cayley tree exhibits unusually weak divergence at the critical point Tc. The susceptibility amplitude is found to diverge at Tc proportionally to the tree generation level n, while the behavior of chi is otherwise analytic in the vicinity of Tc, with the critical exponent gamma=0.