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

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.