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

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

2005-04-07

arxiv.org/abs/cond-mat/0504161v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure

Scientific paper

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.

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