In this chapter we give main definitions and useful facts of the theory of Gibbs measures of
lattice spin systems. In the first section we give general definitions. This chapter also …

In this paper, we consider the Ising-Vannimenus model on a Cayley tree of order three. We
provide an efficient approach to give some explicit formulas for the free energies and the …

In this short research, we delve into the phase transition phenomenon by analyzing the
stability of the dynamical system associated with the (2, 1/2)-mixed spin Ising model on a …

It is known that the disordered phase of the classical Ising model on the Caley tree is
extreme in some region of the temperature. If one considers the Ising model with competing …

In this investigation, we consider the one-dimensional (1D) mixed-type Potts-SOS model,
where the spin is within the range of {− 1, 0, 1}. We elaborate thermodynamic characteristics …

In this paper, we consider the Ising–Vannimenus model on a Cayley tree for order two with
competing nearest-neighbor and prolonged next-nearest neighbor interactions. We stress …

In this paper, we introduce an Ising model with mixed spin (s, 1/2)(abbreviated as (s, 1/2)-
MSIM) for any spin set [− s, s]∩ Z on a semi-infinite second-order Cayley tree and construct …

Ising model with competing nearest–neighbors (NN) and prolonged next–nearest–
neighbors (NNN) interactions on a Cayley tree has long been studied, but there are still …

In this paper, we consider Vannimenus model with competing nearest-neighbors and
prolonged next-nearest-neighbors interactions on a Cayley tree. For this model we define …

In this paper, we consider the Ising-Vanniminus model on an arbitrary-order Cayley tree. We
generalize the results conjectured by Akın [Chinese J. Phys. 54 (4), 635–649 (2016) and Int …