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

2005/04/07 by Borko Stošić, Borko D. Stosic, Stosic, Borko D. +6
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0504161

4 pages, 1 figure

arxiv created 2005/04/07 · arxiv updated 2009/12/01

Abstract

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 T₂=2k_B^-1Jln (√ 2+1) and T_BP=k_B^-1Jln (3), and a line of fourth order phase transitions between T_BP and ∞, where k_B is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.

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