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 …

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 …

Metamaterials, tunable artificial materials, are useful playgrounds to investigate magnetic
systems. So far, artificial Ising spin systems have revealed features such as emergent …

The paper concerns the q-state Potts model (ie with spin values in) on a Cayley tree of
degree (ie with k+ 1 edges emanating from each vertex) in an external (possibly random) …

The progression of cancer in the breast involves multiple reciprocal interactions between
malignantly transformed epithelia, surrounding untransformed but affected stromal cells, and …

The CompuCell3D modeling environment provides a convenient platform for biofilm
simulations using the Glazier-Graner-Hogeweg (GGH) model, a cell-oriented framework …

In this survey, we give a friendly introduction from a graph theory perspective to the q-state
Potts model. The Potts model is an important statistical mechanics tool for analyzing …

Discrete Markov random fields are undirected graphical models in which the nodes of a
graph are discrete random variables with values usually represented by colors. Typically …

A two-dimensional Ising model with nearest-neighbors ferromagnetic interactions is
implemented in a Field Programmable Gate Array (FPGA) board. Extensive Monte Carlo …

We implemented a GPU-based parallel code to perform Monte Carlo simulations of the two-
dimensional q-state Potts model. The algorithm is based on a checkerboard update scheme …