In this paper, we consider the Ising model on a Cayley tree in the presence of competing
binary and prolonged ternary interactions and triple effective local external fields (TELEFs) …

We consider the ferromagnetic Ising model with spatially dependent external fields on a
Cayley tree, and we investigate the conditions for the existence of the phase transition for a …

This work is concerned with the theory of graphical representation for the Ising and Potts
models over general lattices with non-translation invariant external field. We explicitly …

In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in
the presence of a space dependent magnetic field that vanishes as| x|^-α| x|-α, α> 0 α> 0, as …

We extend a recent argument by Ding and Zhuang from nearest-neighbor to long-range
interactions and prove the phase transition in a class of ferromagnetic random field Ising …

In this thesis, we present results on phase transition for two models: the semi-infinite Ising
model with a decaying field, and the long-range Ising model with a random field. We study …

We consider ferromagnetic long-range Ising models which display phase transitions. They
are one-dimensional Ising ferromagnets, in which the interaction is given by J_ x, y= J (| xy|) …

In this thesis, we present results from the investigation of two problems, one related to the
phase transition of long-range Ising models and the other one associated with the …

We consider polynomial long-range Ising models in one dimension, with ferromagnetic pair
interactions decaying with power $2-\alpha $(for $0\leq\alpha< 1$), and prepared with …

Using the group structure of the state space of $ q-$ state models and a new definition of
contour for long-range spin-systems in $\mathbb {Z}^ d $, with $ d\geq 2$, a …