Related papers: Spatiotemporal Patterns in Active Four-State Potts…
The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular…
Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple…
We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant…
We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, $5$, $6$, and $8$ using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the…
We present extensive numerical simulations of a family of non-equilibrium Potts models with absorbing states that allows for a variety of scenarios, depending on the number of spin states and the range of the spin-spin interactions. These…
Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. We consider that molecules bind to either surface of a bilayer membrane and move to the opposite leaflet by flip--flop. When binding does not modify…
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…
Spatial evolution is investigated in a simulated system of nine competing and mutating bacterium strains, which mimics the biochemical war among bacteria capable of producing two different bacteriocins (toxins) at most. Random sequential…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
An asymmetric generalization of the zero-temperature q-state Potts model on a one dimensional lattice, with and without boundaries, has been studied. The dynamics of the particle number, and specially the large time behavior of the system…
We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In…
Two dimensional Potts model is a classical example where the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbours interaction, when the number of states $q$ is less than or…
We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…
We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. We focus on melting process starting from the perfect ordered state. This model is regarded as a standard model to analyze…
Robust phases of matter, which remain stable under small perturbations, are of fundamental importance in statistical physics and quantum information. Recent advances in interactive quantum dynamics have led to renewed interest in…
We investigate slow non-equilibrium dynamical processes in two-dimensional $q$--state Potts model with both ferromagnetic and $\pm J$ couplings. Dynamical properties are characterized by means of the mean-flipping time distribution. This…
We study the non-equilibrium steady states that emerge when two interacting three-dimensional Potts blocks slide on each other. As at equilibrium the Potts model exhibits different types of phase transitions for different numbers $q$ of…
We study a three-state Potts model extended by allowing cyclic dominance between the states as it appears for the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice when varying the temperature and the…
We study a one-dimensional, nonequilibrium Potts-like model which has $q$ symmetric absorbing states. For $q=2$, as expected, the model belongs to the parity conserving universality class. For $q=3$ the critical behaviour depends on the…