Related papers: A classification of four-state spin edge Potts mod…
Machine-learning (ML) models trained on Ising spin configurations have demonstrated surprising effectiveness in classifying phases of Potts models, even when processing severely reduced representations that retain only two spin states. To…
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning…
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…
This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…
The three-state Potts model is numerically investigated on three-dimensional simple cubic lattices of up to \(128^3\) volume, concentrating on the neighborhood of the first-order phase transition separating the ordered and disordered…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
The conventional spin dynamics simulations are performed in direct products of state spaces of individual spins. In a general system of n spins, the total number of elements in the state basis is >4^n. A system propagation step requires an…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
We present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the $q$ states of the ordinary Potts model, this possesses $r$ additional states which contribute to the entropy, but not to the…
The analysis of stability of community structure is an important problem for scientists from many fields. Here, we propose a new framework to reveal hidden properties of community structure by quantitatively analyzing the dynamics of Potts…
We explore the topological defects of the critical three-state Potts spin system on the torus, Klein bottle and cylinder. A complete characterization is obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d rational CFT…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
We use a random pinning procedure to investigate stable glassy states associated with large deviations of the activity in a model glass-former. We pin particles both from active (equilibrium) configurations and from stable (inactive) glassy…
We investigate by means of Monte Carlo simulations the fully connected p-state Potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the, exactly known, behavior of the…
We consider Potts model, with competing interactions and countable spin values $\Phi=\{0,1,\dots \}$ on a Cayley tree of order three. We study periodic ground states for this model.
We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the…
New homotopy approach to the analysis of nonlinear higher-spin equations is developed. It is shown to directly reproduce the previously obtained local vertices. Simplest cubic (quartic in Lagrangian nomenclature) higher-spin interaction…
We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are…