Susceptibilities for the M\"uller-Hartmann-Zitartz countable infinity of phase transitions on a Cayley tree

TL;DR

This paper derives explicit susceptibilities for an infinite set of phase transitions in a Cayley tree model, revealing their physical nature and behavior in the thermodynamic limit.

Contribution

It provides a detailed analytical calculation of susceptibilities for multiple phase transitions in the M"uller-Hartmann-Zitartz model on a Cayley tree, clarifying their physical interpretation.

Findings

Susceptibilities tend to zero above transition temperatures.

Susceptibilities tend to infinity below transition temperatures.

Explicit formulas for susceptibilities are derived for each transition.

Abstract

We obtain explicit susceptibilities for the countable infinity of phase transition temperatures of M\"{u}ller-Hartmann-Zitartz on a Cayley tree. The susceptibilities are a product of the zeroth spin with the sum of an appropriate set of averages of spins on the outermost layer of the tree. A clear physical understanding for these strange phase transitions emerges naturally. In the thermodynamic limit, the susceptibilities tend to zero above the transition and to infinity below it.