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Journal of Magnetism and Magnetic Materials

Tri-critical behaviour of the BEG model on a diamond lattice

M. Kerouad, M. Saber, J.W. Tucker

Published Apr 1, 1995• 8 citations
Publisher
DOI
10.1016/0304-8853(94)01662-3

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We study the phase diagram of the 3-matrix model. This model corresponds to the Blume-Emery-Griffiths (BEG) model on a random surface. The BEG model has parameters J and K which are the spin and the lattice-gas coupling respectively. If K = 0, it is the usual tri-critical Ising model. If K/J = 3, this model becomes the 3-state Potts model. These models are solved in the context of the Coulomb gas representation. The intermediate region K/J = 1 is equivalent to the 3-matrix chain model and we can solve it exactly using the orthogonal polynomial method. We find the 3rd order critical line on which the spin ordering phase transition occurs. This line ends at the 4th order critical point which corresponds to the tri-critical point of the BEG model. The phase diagram is quite similar to that of the BEG model on a regular lattice.
Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.