arXiv subjects

Jeferson J. Arenzon

Publications and source records attributed to Jeferson J. Arenzon.

At least 37 records · Page 2Linked to original sources

arXiv2014

Percolation and cooperation with mobile agents: Geometric and strategy clusters

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius rP, which accounts for the population viscosity, and an interaction radius rint, which defines the instantaneous contact network for the game dynamics. We show that, differently from the rP=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.

physics.soc-ph↗

arXiv2014

Globally synchronized oscillations in complex cyclic games

The Rock-Paper-Scissors (RPS) game and its generalizations with ${\cal S}>3$ species are well studied models for cyclically interacting populations. Four is, however, the minimum number of species that, by allowing other interactions beyond the single, cyclic loop, breaks both the full intransitivity of the food graph and the one predator, one prey symmetry. Lütz {\it et al} (J. Theor. Biol. {\bf 317} (2013) 286) have shown the existence, on a square lattice, of two distinct phases, with either four or three coexisting species. In both phases, each agent is eventually replaced by one of its predators but these strategy oscillations remain localized as long as the interactions are short ranged. Distant regions may be either out of phase or cycling through different food web subloops (if any). Here we show that upon replacing a minimum fraction $Q_c$ of the short range interactions by long range ones, there is a Hopf bifurcation and global oscillations become stable. Surprisingly, to build such long distance, global synchronization, the four species coexistence phase requires less long range interactions than the three species phase, while one would naively expect the contrary. Moreover, deviations from highly homogeneous conditions ($χ=0$ or 1) increase $Q_c$ and the more heterogeneous is the food web, the harder the synchronization is. By further increasing $Q$, while the three species phase remains stable, the four species one has a transition to an absorbing, single species state. The existence of a phase with global oscillations for ${\cal S}>3$, when the interaction graph has multiple subloops and several possible local cycles, lead to the conjecture that global oscillations are a general characteristic, even for large, realistic food webs.

q-bio.PE↗

arXiv2014

Percolation approach to glassy dynamics with continuously broken ergodicity

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F12 schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields new predictions for dynamic relaxation exponents below an upper critical dimension of 6.

cond-mat.stat-mech↗

arXiv2014

Kosterlitz-Thouless and Potts transitions in a generalized XY model

We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso {\it et al} [PRL 106(2011)067202]. Using finite size scaling and focusing on the $q=3$ case, we locate the transitions between the paramagnetic (P), the nematic-like (N) and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the 3-states Potts universality class.

cond-mat.stat-mech↗

arXiv2013

Intransitivity and coexistence in four species cyclic games

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity.

q-bio.PE↗

arXiv2012

Microscopic models of mode-coupling theory: the $F_{12}$ scenario

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the ${\mathsf F}_{12}$ schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamic glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamic facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the ${\mathsf F}_{13}$ schematic model.

cond-mat.dis-nn↗

arXiv2011

Geometrical properties of Potts model during the coarsening regime

We study the dynamic evolution of geometric structures in a poly-degenerate system represented by a $q$-state Potts model with non-conserved order parameter that is quenched from its disordered into its ordered phase. The numerical results obtained with Monte Carlo simulations show a strong relation between the statistical properties of hull perimeters in the initial state and during coarsening: the statistics and morphology of the structures that are larger than the averaged ones are those of the initial state while the ones of small structures are determined by the curvature driven dynamic process. We link the hull properties to the ones of the areas they enclose. We analyze the linear von-Neumann--Mullins law, both for individual domains and on the average, concluding that its validity, for the later case, is limited to domains with number of sides around 6, while presenting stronger violations in the former case.

cond-mat.dis-nn↗

arXiv2011

Glassy dynamics and hysteresis in a linear system of orientable hard rods

We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is coupled to an external field. The equilibrium properties of our model are essentially those of the Tonks gas, but at high densities, the orientational degrees of freedom become effectively frozen due to jamming. This is a simple analytically tractable model of glassy phase. Under a cyclic variation of the pressure, hysteresis is observed. Following a pressure quench, the orientational persistence exhibits a two-stage decay characteristic of glassy systems.

cond-mat.dis-nn↗

arXiv2011

New ordered phases in a class of generalized XY models

It is well known that the 2D XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase transition in the Ising universality class [D.H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985)]. Using a combination of extensive Monte Carlo simulations and finite size scaling, we show that the higher order harmonics lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and pseudonematic couplings. The new phase transitions belong to the 2D Potts, Ising, or KT universality classes.

cond-mat.stat-mech↗

arXiv2010

Dynamic facilitation picture of a higher-order glass singularity

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a hybrid glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions.

cond-mat.dis-nn↗

arXiv2009

Curvature-driven coarsening in the two dimensional Potts model

We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the $q$-states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with non-conserved order parameter. We analyze the distribution of hull enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for $q=2$ (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit super-universality properties.

cond-mat.stat-mech↗

arXiv2008

Geometry of phase separation

We study the domain geometry during spinodal decomposition of a 50:50 binary mixture in two dimensions. Extending arguments developed to treat non-conserved coarsening, we obtain approximate analytic results for the distribution of domain areas and perimeters during the dynamics. The main approximation is to regard the interfaces separating domains as moving independently. While this is true in the non-conserved case, it is not in the conserved one. Our results can therefore be considered as a first-order approximation for the distributions. In contrast to the celebrated Lifshitz-Slyozov-Wagner distribution of structures of the minority phase in the limit of very small concentration, the distribution of domain areas in the 50:50 case does not have a cut-off. Large structures (areas or perimeters) retain the morphology of a percolative or critical initial condition, for quenches from high temperatures or the critical point respectively. The corresponding distributions are described by a $c A^{-τ}$ tail, where $c$ and $τ$ are exactly known. With increasing time, small structures tend to have a spherical shape with a smooth surface before evaporating by diffusion. In this regime the number density of domains with area $A$ scales as $A^{1/2}$, as in the Lifshitz-Slyozov-Wagner theory. The threshold between the small and large regimes is determined by the characteristic area, ${\rm A} \sim [λ(T) t]^{2/3}$. Finally, we study the relation between perimeters and areas and the distribution of boundary lengths, finding results that are consistent with the ones summarized above. We test our predictions with Monte Carlo simulations of the 2d Ising Model.

cond-mat.stat-mech↗

arXiv2008

Random mobility and spatial structure often enhance cooperation

The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population, sometimes promoting, sometimes inhibiting cooperation. Here we show that random dilution and mobility may suppress the inhibiting factors of the spatial structure in the Snowdrift game, while enhancing the already larger cooperation found in the Prisoner's dilemma and Stag Hunt games.

q-bio.PE↗

arXiv2008

Experimental test of curvature-driven dynamics in the phase ordering of a two dimensional liquid crystal

We study electric field driven deracemization in an achiral liquid crystal through the formation and coarsening of chiral domains. It is proposed that deracemization in this system is a curvature-driven process. We test this prediction using the exact result for the distribution of hull-enclosed areas in two-dimensional coarsening in non-conserved scalar order parameter dynamics recently obtained [J.J. Arenzon et al., Phys. Rev. Lett. 98, 061116 (2007)]. The experimental data are in very good agreement with the theory. We thus demonstrate that deracemization in such bent-core liquid crystals belongs to the Allen-Cahn universality class, and that the exact formula, which gives us the statistics of domain sizes during coarsening, can also be used as a strict test for this dynamic universality class.

cond-mat.dis-nn↗

arXiv2007

Geometric properties of two-dimensional coarsening with weak disorder

The domain morphology of weakly disordered ferromagnets, quenched from the high-temperature phase to the low-temperature phase, is studied using numerical simulations. We find that the geometrical properties of the coarsening domain structure, e.g., the distributions of hull enclosed areas and domain perimeter lengths, are described by a scaling phenomenology in which the growing domain scale R(t) is the only relevant parameter. Furthermore, the scaling functions have forms identical to those of the corresponding pure system, extending the 'super-universality' property previously noted for the pair correlation function.

cond-mat.dis-nn↗

arXiv2007

Domain growth morphology in curvature driven two dimensional coarsening

We study the distribution of domain areas, areas enclosed by domain boundaries (''hulls''), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, $n_h(A,t) dA$, with enclosed area in the interval $(A,A+dA)$, is described, for a disordered initial condition, by the scaling function $n_h(A,t) = 2c_h/(A + λ_h t)^2$, where $c_h=1/8π\sqrt{3} \approx 0.023$ is a universal constant and $λ_h$ is a material parameter. For a critical initial condition, the same form is obtained, with the same $λ_h$ but with $c_h$ replaced by $c_h/2$. For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form $n_d(A,t) = 2c_d (λ_d t)^{τ'-2}/(A + λ_d t)^{τ'}$, where $c_d=c_h + {\cal O}(c_h^2)$, $λ_d=λ_h + {\cal O}(c_h)$, and $τ' = 187/91 \approx 2.055$. For critical initial conditions, one replaces $c_d$ by $c_d/2$ (possibly with corrections of ${\cal O}(c_h^2)$) and the exponent is $τ= 379/187 \approx 2.027$. These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.

cond-mat.stat-mech↗

arXiv2007

Exact results for curvature-driven coarsening in two dimensions

We consider the statistics of the areas enclosed by domain boundaries (`hulls') during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than $A$ has, for large time $t$, the scaling form $N_h(A,t) = 2c/(A+λt)$, demonstrating the validity of dynamical scaling in this system, where $c=1/8π\sqrt{3}$ is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of $A/λt$. Identical forms are obtained for coarsening from a critical initial state, but with $c$ replaced by $c/2$.

cond-mat.stat-mech↗

arXiv2006

Monte Carlo simulations of 2d hard core lattice gases

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, $λ$ (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class -- contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.

cond-mat.stat-mech↗