Third and Fourth Order Phase Transitions: Exact Solution for the Ising Model on the Cayley Tree

Stosic, Borko D.; Stosic, Tatijana; Fittipaldi, Ivon P.

Third and Fourth Order Phase Transitions: Exact Solution for the Ising Model on the Cayley Tree

Authors

Stosic, Borko D.

Stosic, Tatijana

Fittipaldi, Ivon P.

Description

An exact analytical derivation is presented, showing that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures $T_2=2k_B^{-1}J\ln ({\sqrt 2}+1) $ and $T_{BP}=k_B^{-1}J\ln (3)$, and a line of fourth order phase transitions between $T_{BP}$ and $\infty$, where $k_B$ is the Boltzmann constant, and $J$ is the nearest-neighbor interaction parameter.
4 pages, 1 figure