arXiv subjects

Gyorgy Szabo

Publications and source records attributed to Gyorgy Szabo.

51 records · Page 3Linked to original sources

arXiv2001

A three-state cyclic voter model extended with Potts energy

The cyclically dominated voter model on a square lattice is extended by taking into consideration the variation of Potts energy during the nearest neighbor invasions. We have investigated the effect of surface tension on the self- organizing patterns maintained by cyclic invasions. A geometrical analysis is also developed tp study the three-color patterns. These investigations indicate clearly that in the "voter model" limit the pattern evolution is governed by the loop creation due to the overhanging during the interfacial roughening. Conversely, in the presence surface tension the evolution is governed by spiral formation whose geometrical parameters depend on the strength of cyclic dominance.

cond-mat.stat-mech↗

arXiv2000

Branching annihilating random walk on random regular graphs

The branching annihilating random walk is studied on a random graph whose sites have uniform number of neighbors (z). The Monte Carlo simulations in agreement with the generalized mean-field analysis indicate that the concentration decreses linearly with the branching rate for $z \ge 4$ while the coefficient of the linear term becomes zero if $z=3$. These features are described by a modified mieb-field theory taking explicitly into consideration the probability of mutual annihilation of the parent and its offspring particles using the returning features of a single walker on the same graph.

cond-mat.stat-mech↗

arXiv2000

Phase transition in a spatial Lotka-Volterra model

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 dynamics on a square lattice is governed by very symmetrical transition rules for neighborhood invasion of sensitive strains by killers, killers by resistants, and resistants by by sensitives. The community of the nine possible toxicity/resistance types undergoes a critical phase transition as the uniform transmutation rates between the types decreases below a critical value $P_c$ above which all the nine types of strain coexist with equal frequencies. Passing the critical mutation rate from above, the system collapses into one of the three topologically identical states, each consisting of three strain types. Of the three final states each accrues with equal probability and all three maintain themselves in a self-organizing polydomain structure via cyclic invasions. Our Monte Carlo simulations support that this symmetry breaking transition belongs to the universality class of the three-state Potts model.

cond-mat.stat-mech↗

arXiv2000

Spatial evolutionary prisoner's dilemma game with three strategies and external constraints

The emergence of mutual cooperation is studied in a spatially extended evolutionary prisoner's dilemma game in which the players are located on the sites of cubic lattices for dimensions d=1, 2, and 3. Each player can choose one of the three strategies: cooperation (C), defection (D) or Tit for Tat (T). During the evolutionary process the randomly chosen players adopt one of their neighboring strategies if the chosen neighbor has higher payoff. Morover, an external constraint imposes that the players always cooperate with probability p. The stationary state phase diagram are computed by both using generalized mean-field approximations and Monte Carlo simulations. Nonequilibrium second order phase transitions assosiated with the extinction of one of the possible strategies are found and the corresponding critical exponents belong to the directed percolation universality class. It is shown that forcing externally the collaboration does not always produce the desired result.

cond-mat.stat-mech↗

arXiv1999

Vortex dynamics in a three-state model under cyclic dominance

The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate which is increased by the spiral formation due to the cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle antiparticle system with density dependent pair creation rate. Numerical estimates for the critical indices of the vortex density ($β=0.29(4)$) and of its fluctuation ($γ=0.34(6)$) improve an earlier Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic voter model in two dimensions.

cond-mat.stat-mech↗

arXiv1999

Branching annihilating random walks with parity conservation on a square lattice

Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the first model the randomly walking particles annihilate when they meet and the branching process creates two additional particles; in the second case we distinguish particles and antiparticles created and annihilated in pairs. Quite distinct critical behavior is found in the two cases, raising the question of what determines universality in this kind of systems.

cond-mat.stat-mech↗

arXiv1998

Magnetic hysteresis in Ising-like dipole-dipole model

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis and allowed us to have a deeper insight into the series of metastable states developed during this process.

cond-mat↗

arXiv1997

Evolutionary prisoner's dilemma game on a square lattice

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques we study the density $c$ of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing state when varying the value of temptation to defect. In the limits $c \to 0$ and 1 we have observed critical transitions belonging to the universality class of directed percolation.

cond-mat.stat-mech↗

arXiv1996

Critical domain size in a driven diffusive system

The homogeneous ordered state transforms into a polydomain state via a nucleation mechanism in two-dimensional lattice gas if the particle jumps are biased by an external field $E$. A simple phenomenological model is used to describe the time evolution of a circular interface separating the ordered regions. It is shown that the area of a domain increases if its radius exceeds a critical value proportional to $1/E$ which agrees qualitatively with Monte Carlo simulations.

cond-mat↗

arXiv1995

Entropy derivation for cluster methods in non-Bravais lattices

The derivation of entropy for cluster methods is reformulated by constructing the probability of a given particle (spin) configuration as a self-consistent product of cluster configuration probabilities. This approach gives an insight into the nature of underlying approximations involved at different levels of the cluster-variation method. The graphical representation of the product allows us to extend this method for non-Bravais lattices as it is demonstrated on interstitial sites of body-centered- and face-centered-cubic crystals.

cond-mat↗

arXiv1995

Lattice-gas model for alkali-metal fullerides: body-centered-cubic structure

A Coulomb lattice-gas model with a host lattice screening mechanism is adapted to describe the ordering phenomena in alkali-metal fullerides of body-centered-cubic structure. It is assumed that the electric charge of an alkali ion residing at a tetrahedral interstitial site is completely screened by its first-neighbor C$_{60}$ molecules. The electronic energy of the C$_{60}^{x-}$ ion is also taken into consideration as a charged spherical shell. By means of these assumptions an effective (short range) pair interaction is obtained between two alkali ions. The resultant lattice-gas model is analyzed by using two- and six-sublattice mean-field approximations. The thermodynamic properties are summarized in phase diagrams for different shell radii.

cond-mat↗

arXiv1995

Lattice-gas model for alkali-metal fullerides: face-centered-cubic structure

A lattice-gas model is suggested for describing the ordering phenomena in alkali-metal fullerides of face-centered-cubic structure assuming the electric charge of alkali ions residing in either octahedral or tetrahedral interstitial sites is completely screened by the first-neighbor C_60 molecules. This approximation allows us to derive an effective ion-ion interaction. The van der Waals interaction between the ion and C_60 molecule is characterized by introducing an additional energy at the tetrahedral sites. This model is investigated by using a three-sublattice mean-field approximation and a simple cluster-variation method. The analysis shows a large variety of phase diagrams when changing the site energy parameter.

cond-mat↗

arXiv1995

Self-organizing domain structure in a driven lattice gas

Instead of the homogeneous ordered particle distributions characteristic to equilibrium systems a self-organizing polydomain structure is found to be stable at low temperatures in a square lattice-gas model with repulsive nearest neighbor interaction when the particle jumps are biased by a uniform electric field. We have performed Monte Carlo simulations to study the domain structure varying the temperatures, fields and system sizes. Revision of the traditional picture on this system raises interesting problems as discussed.

cond-mat↗

arXiv1995

Generalized mean-field study of a driven lattice gas

Generalized mean-field analysis has been performed to study the ordering process in a half-filled square lattice-gas model with repulsive nearest neighbor interaction under the influence of a uniform electric field. We have determined the configuration probabilities on 2-, 4-, 5-, and 6-point clusters excluding the possibility of sublattice ordering. The agreement between the results of 6-point approximations and Monte Carlo simulations confirms the absence of phase transition for sufficiently strong fields.

cond-mat↗

arXiv1995

Anisotropic Ordering in a Two-Temperature Lattice Gas

We consider a two-dimensional lattice gas model with repulsive nearest- and next-nearest-neighbor interactions that evolves in time according to anisotropic Kawasaki dynamics. The hopping of particles along the principal directions is governed by heat baths at different temperatures. The stationary states of this non-equilibrium model are studied using a generalized dynamical mean-field analysis. In the stable state the particles form parallel chains which are oriented along the direction of the higher temperature. The resulting phase diagram is confirmed by Monte Carlo simulations

cond-mat↗