An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model
Department of Physics, Erciyes University, 38039 Kayseri, Turkey
Corresponding author: a email@example.com
Revised: 28 September 2001
Published online: 15 December 2001
A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q=3. The exact phase diagrams in (k T / J, K / J ) and (k T/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (k T / J, K / J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (k T/ J, D / J ) plane.
PACS: 05.70.Fh – Phase transitions: general studies / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 75.10.Hk – Classical spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001