In this paper, we give a systematic review of the theory of Gibbs measures of Potts model on
Cayley trees (developed since 2013) and discuss many applications of the Potts model to …

The positive manifold of intelligence has fascinated generations of scholars in human ability.
In the past century, various formal explanations have been proposed, including the …

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 …

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 …

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 …

arXiv:2009.08129v2 [math.PR] 23 Nov 2020 Page 1 CONFORMAL MEASURE ENSEMBLES
AND PLANAR ISING MAGNETIZATION: A REVIEW FEDERICO CAMIA, JIANPING JIANG, AND …

We study the problem of learning graphical models with latent variables. We give the {\em
first} efficient algorithms for learning: 1) ferromagnetic Ising models with latent variables …

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 …

Following seminal work by J. Fr\" ohlich and T. Spencer on the critical exponent $\alpha= 2$,
we give a proof via contours of phase transition in the one-dimensional long-range …

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|) …