Mukhamedov, Farrukh
(2010)
Lattice models with interactions on Caylay tree.
In: IIUM Research, Innovation & Invention Exhibition (IRIIE 2010), 26 - 27 January 2010, Kuala Lumpur.
Abstract
We consider an Ising competitive model defined over a triangular Husimi tree where loops,
responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model
with fixed couplings in which a “gas of noninteracting dimmers (or spin liquid) — ferro or
antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then
we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We
find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature
phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. On
the other hand, In this investigation we studied one-dimensional countable state p-adic Potts model. We
prove the existence of generalized p-adic Gibbs measures for the given model. It is also shown that under
the condition there may occur a phase transition.
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