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Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree

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  • Stošić, Borko D.
  • Stošić, Tatijana
  • Fittipaldi, Ivon P.

Abstract

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures T2=2kB−1Jln(2+1) and TBP=kB−1Jln(3), and a line of fourth order phase transitions between TBP and ∞, where kB is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.

Suggested Citation

  • Stošić, Borko D. & Stošić, Tatijana & Fittipaldi, Ivon P., 2009. "Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1074-1078.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:7:p:1074-1078
    DOI: 10.1016/j.physa.2008.12.051
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