arXiv subjects

R. Juhász

Publications and source records attributed to R. Juhász.

14 recordsLinked to original sources

arXiv2024

Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal

Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical renormalization group results for the paradigmatic model, the contact process, in the combined presence of these factors in both one and two-dimensional systems. Our results confirm our analytic arguments stating that the density vanishes smoothly at the extinction threshold, in a way characteristic of infinite-order transitions. This extremely smooth vanishing of the global density entails an enhanced exposure of the population to extinction events. At the same time, a reverse order parameter, the local persistence displays a discontinuity characteristic of mixed-order transitions, as it approaches a non-universal critical value algebraically with an exponent $β_p'<1$.

cond-mat.stat-mech↗

arXiv2023

Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields

In transverse-field Ising models, disorder in the couplings gives rise to a drastic reduction of the critical energy gap and, accordingly, to an unfavorable, slower-than-algebraic scaling of the density of defects produced when the system is driven through its quantum critical point. By applying Kibble-Zurek theory and numerical calculations, we demonstrate in the one-dimensional model that the scaling of defect density with annealing time can be made algebraic by balancing the coupling disorder with suitably chosen inhomogeneous driving fields. Depending on the tail of the coupling distribution at zero, balancing can be either perfect, leading to the well-known inverse-square law of the homogeneous system, or partial, still resulting in an algebraic decrease but with a smaller, non-universal exponent. We also study defect production during an environment-temperature quench of the open variant of the model in which the system is slowly cooled down to its quantum critical point. According to our scaling and numerical results, balanced disorder leads again to an algebraic temporal decrease of the defect density.

cond-mat.stat-mech↗

arXiv2020

Percolation theory suggests some general features in range margins across environmental gradients

The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range margins is fragmentation, caused internally by population dynamics or externally by the limited availability of suitable habitat sites. We study both causes, and describe the transition from a connected to a fragmented state across space by means of a gradient metapopulation model. The main features of our approach are the following. 1) Inhomogeneities can occur at two spatial scales: there is a broad-scale gradient, which can be patterned by fine-scale heterogeneities. The latter is implemented by dispersing a variable number of small obstacles over the terrain, which can be penetrable or unpenetrable by the spreading species. 2) We study the occupancy of this terrain in a steady-state on two temporal scales: in snapshots and by long-term averages. The simulations reveal some general scaling laws that are applicable in various environments, independently of the mechanism of fragmentation. The edge of the connected region (the hull) is a fractal with dimension 7/4. Its width and length changes with the gradient according to universal scaling laws, that are characteristic for percolation transitions. The results suggest that percolation theory is a powerful tool for understanding the structure of range margins in a broad variety of real-life scenarios, including those in which the environmental gradient is combined with fine-scale heterogeneity. This provides a new method for comparing the range margins of different species in various geographic regions, and monitoring range shifts under climate change.

q-bio.PE↗

arXiv2020

Population boundary across an environmental gradient: Effects of quenched disorder

Population boundary is a classic indicator of climatic response in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental factors, but also by local heterogeneities in the regional characteristics. Here, we capture the effects of quenched heterogeneities on the ecological boundary with the disordered contact process in one and two dimensions with a linear spatial trend in the local control parameter. We apply the strong-disorder renormalization group method to calculate the sites occupied with an $O(1)$ probability in the stationary state, readily yielding the population front's position as the outermost site locally as well as globally for the entire boundary. We show that under a quasistatic change of the global environment, mimicking climate change, the front advances intermittently: long quiescent periods are interrupted by rare but long jumps. The characteristics of this intermittent dynamics are found to obey universal scaling laws in terms of the gradient, conjectured to be related to the correlation-length exponent of the model. Our results suggest that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change.

q-bio.PE↗

arXiv2019

Critical dynamics of the Kuramoto model on sparse random networks

We consider the Kuramoto model on sparse random networks such as the Erdős-Rényi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition by large-scale, massively parallel numerical integration. By this method, we obtain an estimate of critical coupling strength more accurate than obtained earlier by finite-size scaling of the stationary order parameter. Our results confirm the compatibility of the correlation-size and the temporal correlation-length exponent with the mean-field universality class. However, the scaling of the order parameter exhibits corrections much stronger than those of the Kuramoto model with all-to-all coupling, making thereby an accurate estimate of the order-parameter exponent hard. We find furthermore that, as a qualitative difference to the model with all-to-all coupling, the effective critical exponents involving the order-parameter exponent, such as the effective decay exponent characterizing the critical desynchronization dynamics show a non-monotonic approach toward the asymptotic value. In the light of these results, the technique of finite-size scaling of limited size data for the Kuramoto model on sparse graphs has to be treated cautiously.

cond-mat.stat-mech↗

arXiv2018

Nonuniversal and anomalous critical behavior of the contact process near an extended defect

We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $λ(l)-λ(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate on the marginal situation, $s=1/ν_{\perp}$, where $ν_{\perp}$ is the critical exponent of the spatial correlation length, and study the local critical properties of the one-dimensional model by Monte Carlo simulations. The system exhibits a rich surface critical behavior. For weaker local activation rates, $A A_c$, the phase transition is of mixed order: the surface order parameter is discontinuous, at the same time the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. The mixed-order transition regime is analogous to that observed recently at a multiple junction and can be explained by the same type of scaling theory.

cond-mat.stat-mech↗

arXiv2017

Mixed-order phase transition of the contact process near multiple junctions

We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant ($M=2$) and semi-infinite ($M=1$) system, the local order parameter is found to be discontinuous for $M>2$. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with $M$. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.

cond-mat.stat-mech↗

arXiv2016

Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field

We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave-packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as $t^{1/2}$ and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse-field is changed in discrete time-steps, $τ$, there can be excitation modes, for which coherence is maintained, provided their energy satisfies $ε_k τ\approx nπ$ with a positive integer $n$. If the dispersion of $ε_k$ is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a $t^{3/4}$ time-dependence.

cond-mat.stat-mech↗

arXiv2015

Long-range epidemic spreading in a random environment

Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+σ}$. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as $P(t) \sim t^{-d/z}$ up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent $z$ varies continuously with the control parameter and tends to $z_c=d+σ$ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as $R(t) \sim t^{1/z_c}$ with a multiplicative logarithmic correction, and the average number of infected sites in surviving trials is found to increase as $N_s(t) \sim (\ln t)^χ$ with $χ=2$ in one dimension.

cond-mat.dis-nn↗

arXiv2013

Infinite randomness critical behavior of the contact process on networks with long-range connections

The contact process and the slightly different susceptible-infected-susceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and Monte Carlo simulations. We focus on the case where the connection probability decays with the distance $l$ as $p(l)\simeqβl^{-2}$ in one dimension. Here, the graph dimension of the network can be continuously tuned with $β$. The critical behavior of the models is found to be described by an infinite randomness fixed point which manifests itself in logarithmic dynamical scaling. Estimates of the complete set of the critical exponents, which are found to vary with the graph dimension, are provided by different methods. According to the results, the additional disorder of transition rates does not alter the infinite randomness critical behavior induced by the disordered topology of the underlying random network. This finding opens up the possibility of the application of an alternative tool, the strong disorder renormalization group method to dynamical processes on topologically disordered structures. As the random transverse-field Ising model falls into the same universality class as the random contact process, the results can be directly transferred to that model defined on the same networks.

cond-mat.dis-nn↗

arXiv2012

Anomalous coarsening in disordered exclusion processes

We study coarsening phenomena in three different simple exclusion processes with quenched disordered jump rates. In the case of the totally asymmetric process, an earlier phenomenological description is improved, yielding for the time dependence of the length scale $ξ(t)\sim t/(\ln t)^2$, which is found to be in agreement with results of Monte Carlo simulations. For the partially asymmetric process, the logarithmically slow coarsening predicted by a phenomenological theory is confirmed by Monte Carlo simulations and numerical mean-field calculations. Finally, coarsening in a bidirectional, two-lane model with random lane-change rates is studied. Here, Monte Carlo simulations indicate an unusual dependence of the dynamical exponent on the density of particles.

cond-mat.dis-nn↗

arXiv2010

Anomalous diffusion in disordered multi-channel systems

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong disorder renormalization group method and Monte Carlo simulations are used. Generally, we observe anomalous diffusion, where the average distance travelled by the particle, [ ]_{av}, has a power-law time-dependence [ ]_{av} ~ t^{μ_K(v)}, with a diffusion exponent 0 \le μ_K(v) \le 1. In the presence of left-right symmetry of the distribution of random rates, the recurrent point of the multi-channel system is independent of K, and the diffusion exponent is found to increase with K and decrease with v. In the absence of this symmetry, the recurrent point may be shifted with K and the current can be reversed by varying the lane change rate v.

cond-mat.dis-nn↗

arXiv2009

Scaling behavior of the contact process in networks with long-range connections

We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that are characterized by different shortest-path dimensions and random-walk dimensions. We provide numerical evidence that an absorbing phase transition occurs at some finite value of the infection rate and the corresponding dynamical critical exponents depend on the underlying network. Furthermore, the time-dependent quantities exhibit log-periodic oscillations in agreement with the discrete scale invariance of the networks. In case of spreading from an initial active seed, the critical exponents are found to depend on the location of the initial seed and break the hyper-scaling law of the directed percolation universality class due to the inhomogeneity of the networks. However, if the cluster spreading quantities are averaged over initial sites the hyper-scaling law is restored.

cond-mat.stat-mech↗

arXiv2008

Exact relationship between the entanglement entropies of XY and quantum Ising chains

We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of l spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.

cond-mat.stat-mech↗