Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions - Ganikhodjaev, Nasir (EUDOXUS PRESS, LLC, 2010)
We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al [2] generalized this result for Ising model with Jo 6= 0 and recently anikhodjaev et al [3] proved similar result for the three-state Potts model with Jo = 0. For given lattice model on a Cayley tree we produce recursive relations obtained following the lines of Inawashiro et al [4]. These recursive relations provide us the numerically exact phase diagram of the model. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of J2/J1, J3/J1.