arXiv subjects

Róbert Juhász

Publications and source records attributed to Róbert Juhász.

At least 37 records · Page 2Linked to original sources

arXiv2015

Competition between quenched disorder and long-range connections: A numerical study of diffusion

The problem of random walk is considered in one dimension in the simultaneous presence of a quenched random force field and long-range connections the probability of which decays with the distance algebraically as p_l ~ βl^{-s}. The dynamics are studied mainly by a numerical strong disorder renormalization group method. According to the results, for s>2 the long-range connections are irrelevant and the mean-square displacement increases as ~ (ln t)^{2/ψ} with the barrier exponent ψ=1/2, which is known in one-dimensional random environments. For s<2, instead, the quenched disorder is found to be irrelevant and the dynamical exponent is z=1 like in a homogeneous environment. At the critical point, s=2, the interplay between quenched disorder and long-range connections results in activated scaling, however, with a non-trivial barrier exponent ψ(β), which decays continuously with β, but is independent of the form of the quenched disorder. Upper and lower bounds on ψ(β) are established and numerical estimates are given for various values of β. Beside random walks, accurate numerical estimates of the graph dimension and the resistance exponent are given for various values of βat s=2.

cond-mat.dis-nn↗

arXiv2014

Infinite-disorder critical points of models with stretched exponential interactions

We show that an interaction decaying as a stretched exponential function of the distance, $J(l)\sim e^{-cl^a}$, is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We obtain that the critical behavior of the model is controlled by infinite-disorder fixed points different from that of the short-range one if $0 1/2$, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size $L$ increases logarithmically with $L$ in the critical point but, as opposed to the short-range model, the prefactor is disorder-dependent in the range $0<a<1/2$. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

cond-mat.dis-nn↗

arXiv2014

Random transverse-field Ising chain with long-range interactions

We study the low-energy properties of the long-range random transverse-field Ising chain with ferromagnetic interactions decaying as a power alpha of the distance. Using variants of the strong-disorder renormalization group method, the critical behavior is found to be controlled by a strong-disorder fixed point with a finite dynamical exponent z_c=alpha. Approaching the critical point, the correlation length diverges exponentially. In the critical point, the magnetization shows an alpha-independent logarithmic finite-size scaling and the entanglement entropy satisfies the area law. These observations are argued to hold for other systems with long-range interactions, even in higher dimensions.

cond-mat.dis-nn↗

arXiv2014

Critical behavior of models with infinite disorder at a star junction of chains

We study two models having an infinite-disorder critical point --- the zero temperature random transverse-field Ising model and the random contact process --- on a star-like network composed of $M$ semi-infinite chains connected to a common central site. By the strong disorder renormalization group method, the scaling dimension $x_M$ of the local order parameter at the junction is calculated. It is found to decrease rapidly with the number $M$ of arms, but remains positive for any finite $M$. This means that, in contrast with the pure transverse-field Ising model, where the transition becomes of first order for $M>2$, it remains continuous in the disordered models, although, for not too small $M$, it is hardly distinguishable from a discontinuous one owing to a close-to-zero $x_M$. The scaling behavior of the order parameter in the Griffiths-McCoy phase is also analyzed.

cond-mat.dis-nn↗

arXiv2014

Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments

We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched survival probability $\mathcal{P}(t)$ defined in fixed random environments is found to show multi-scaling in the critical point, meaning that $\mathcal{P}(t)=t^{-δ}$, where the (environment and time-dependent) exponent $δ$ has a universal limit distribution when $t\to\infty$. The limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi-infinite lattice, where it is found to be exponential, while, in the infinite system, conjectures on its limiting behaviors for small and large $δ$, which are based on numerical results, are formulated. By the same method, the quenched survival probability in the problem of {\it random walks in random environments} is also shown to exhibit multi-scaling with an exponential limit distribution. In addition to this, the (imaginary-time) spin-spin autocorrelation function of the {\it random transverse-field Ising chain} is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach. Consequently, a relationship between the corresponding limit distributions in the two problems can be established. Finally, the distribution of the spontaneous magnetization in this model is also discussed.

cond-mat.dis-nn↗

arXiv2013

Disordered contact process with asymmetric spreading

An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it is shown that the local asymmetry of spreading is irrelevant on large scales if the model is globally (statistically) symmetric. Otherwise, in the presence of a global bias in either direction, the renormalization method predicts two distinct phase transitions, which are related to the spreading of activity in and against the direction of the bias. The latter is found to be described by an infinite randomness fixed point while the former is not.

cond-mat.dis-nn↗

arXiv2012

Rare region effects in the contact process on networks

Networks and dynamical processes occurring on them have become a paradigmatic representation of complex systems. Studying the role of quenched disorder, both intrinsic to nodes and topological, is a key challenge. With this in mind, here we analyse the contact process, i.e. the simplest model for propagation phenomena, with node-dependent infection rates (i.e. intrinsic quenched disorder) on complex networks. We find Griffiths phases and other rare region effects, leading rather generically to anomalously slow (algebraic, logarithmic, etc.) relaxation, on Erdős-Rényi networks. We predict similar effects to exist for other topologies as long as a non-vanishing percolation threshold exists. More strikingly, we find that Griffiths phases can also emerge --even with constant epidemic rates-- as a consequence of mere topological heterogeneity. In particular, we find Griffiths phases in finite dimensional networks as, for instance, a family of generalized small-world networks. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks, and are relevant for the analysis of both models and empirical data.

cond-mat.stat-mech↗

arXiv2012

The effect of asymmetric disorder on the diffusion in arbitrary networks

Considering diffusion in the presence of asymmetric disorder, an exact relationship between the strength of weak disorder and the electric resistance of the corresponding resistor network is revealed, which is valid in arbitrary networks. This implies that the dynamics are stable against weak asymmetric disorder if the resistance exponent $ζ$ of the network is negative. In the case of $ζ>0$, numerical analyses of the mean first-passage time $τ$ on various fractal lattices show that the logarithmic scaling of $τ$ with the distance $l$, $\lnτ\sim l^ψ$, is a general rule, characterized by a new dynamical exponent $ψ$ of the underlying lattice.

cond-mat.dis-nn↗

arXiv2011

Mean field treatment of exclusion processes with random-force disorder

The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with earlier intuitive assumptions. On the grounds of these results, a phenomenological random barrier model is applied in order to describe quantitatively the coarsening phenomena. Predictions of the theory are compared with numerical results obtained by integrating the mean field evolution equations.

cond-mat.dis-nn↗

arXiv2010

Griffiths phases in the contact process on complex networks

Dynamical processes occurring on top of complex networks have become an exciting area of research. Quenched disorder plays a relevant role in general dynamical processes and phase transitions, but the effect of topological quenched disorder on the dynamics of complex networks has not been systematically studied so far. Here, we provide heuristic and numerical analyses of the contact process defined on some complex networks with topological disorder. We report on Griffiths phases and other rare region effects, leading rather generically to anomalously slow relaxation in generalized small-world networks. In particular, it is illustrated that Griffiths phases can emerge as the consequence of pure topological heterogeneity if the topological dimension of the network is finite.

cond-mat.stat-mech↗

arXiv2010

Griffiths phases on complex networks

Quenched disorder is known to play a relevant role in dynamical processes and phase transitions. Its effects on the dynamics of complex networks have hardly been studied. Aimed at filling this gap, we analyze the Contact Process, i.e. the simplest propagation model, with quenched disorder on complex networks. We find Griffiths phases and other rare region effects, leading rather generically to anomalously slow (algebraic, logarithmic, ...) relaxation, on Erd\H os-Rényi networks. Similar effects are predicted to exist for other topologies with a finite percolation threshold. More surprisingly, we find that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of topological heterogeneity in networks with finite topological dimension. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks.

cond-mat.stat-mech↗

arXiv2009

Dynamics at barriers in bidirectional two-lane exclusion processes

A two-lane exclusion process is studied where particles move in the two lanes in opposite directions and are able to change lanes. The focus is on the steady state behavior in situations where a positive current is constrained to an extended subsystem (either by appropriate boundary conditions or by the embedding environment) where, in the absence of the constraint, the current would be negative. We have found two qualitatively different types of steady states and formulated the conditions of them in terms of the transition rates. In the first type of steady state, a localized cluster of particles forms with an anti-shock located in the subsystem and the current vanishes exponentially with the extension of the subsystem. This behavior is analogous to that of the one-lane partially asymmetric simple exclusion process, and can be realized e.g. when the local drive is induced by making the jump rates in two lanes unequal. In the second type of steady state, which is realized e.g. if the local drive is induced purely by the bias in the lane change rates, and which has thus no counterpart in the one-lane model, a delocalized cluster of particles forms which performs a diffusive motion as a whole and, as a consequence, the current vanishes inversely proportionally to the extension of the subsystem. The model is also studied in the presence of quenched disordered, where, in case of delocalization, phenomenological considerations predict anomalously slow, logarithmic decay of the current with the system size in contrast with the usual power-law.

cond-mat.stat-mech↗

arXiv2009

A non-conserving coagulation model with extremal dynamics

A coagulation process is studied in a set of random masses, in which two randomly chosen masses and the smallest mass of the set multiplied by some fixed parameter $ω\in [-1,1]$ are iteratively added. Besides masses (or primary variables), secondary variables are also considered that are correlated with primary variables and coagulate according to the above rule with $ω=0$. This process interpolates between known statistical physical models: The case $ω=-1$ corresponds to the strong disorder renormalisation group transformation of certain disordered quantum spin chains whereas $ω=1$ describes coarsening in the one-dimensional Glauber-Ising model. The case $ω=0$ is related to the renormalisation group transformation of a recently introduced graph with a fat-tail edge-length distribution. In the intermediate range $-1<ω<1$, the exponents $α_ω$ and $β_ω$ that characterise the growth of the primary and secondary variable, respectively, are accurately estimated by analysing the differential equations describing the process in the continuum formulation. According to the results, the exponent $α_ω$ varies monotonically with $ω$ while $β_ω$ has a maximum at $ω=0$.

cond-mat.dis-nn↗

arXiv2009

Superdiffusion in a class of networks with marginal long-range connections

A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively connecting each site of degree 2 with a $k$th neighboring site of degree 2. Specifying the way pairs of sites to be connected are selected, various random and regular networks are defined, all of which have a power-law edge-length distribution of the form $P_>(l)\sim l^{-s}$ with the marginal exponent s=1. In all these networks, lengths of shortest paths grow as a power of the distance and random walk is super-diffusive. Applying a renormalization group method, the corresponding shortest-path dimensions and random-walk dimensions are calculated exactly for k=1 networks and for k=2 regular networks; in other cases, they are estimated by numerical methods. Although, s=1 holds for all representatives of this class, the above quantities are found to depend on the details of the structure of networks controlled by k and other parameters.

cond-mat.dis-nn↗

arXiv2008

Random walks in a random environment on a strip: a renormalization group approach

We present a real space renormalization group scheme for the problem of random walks in a random environment on a strip, which includes one-dimensional random walk in random environment with bounded non-nearest-neighbor jumps. We show that the model renormalizes to an effective one-dimensional random walk problem with nearest-neighbor jumps and conclude that Sinai scaling is valid in the recurrent case, while in the sub-linear transient phase, the displacement grows as a power of the time.

cond-mat.dis-nn↗

arXiv2007

Anomalous transport in disordered exclusion processes with coupled particles

We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on the transport properties in the presence of random-force type disorder by means of a phenomenological random trap picture. In the phase-separated steady state of the model defined on a finite ring, the properties of the density profile are studied and the exponent governing the decay of the current with the system size in the biased phase is derived. In case all consecutive particles are coupled with each other and form a closed string, the current is found to be enhanced compared to the model without coupling, while if groups of consecutive particles form finite strings, the current is reduced. The motion of a semi-infinite string entering an initially empty lattice is also studied. Here, the diffusion of the head of the string is found to be anomalous, and two phases can be distinguished, which are characterised by different functional dependences of the diffusion exponent on the bias. The obtained results are checked by numerical simulation.

cond-mat.dis-nn↗

arXiv2007

Entanglement entropy in aperiodic singlet phases

We study the average entanglement entropy of blocks of contiguous spins in aperiodic XXZ chains which possess an aperiodic singlet phase at least in a certain limit of the coupling ratios. In this phase, where the ground state constructed by a real space renormalization group method, consists (asymptotically) of independent singlet pairs, the average entanglement entropy is found to be a piecewise linear function of the block size. The enveloping curve of this function is growing logarithmically with the block size, with an effective central charge in front of the logarithm which is characteristic for the underlying aperiodic sequence. The aperiodic sequence producing the largest effective central charge is identified, and the latter is found to exceed the central charge of the corresponding homogeneous model. For marginal aperiodic modulations, numerical investigations performed for the XX model show a logarithmic dependence, as well, with an effective central charge varying continuously with the coupling ratio.

cond-mat.stat-mech↗

arXiv2006

Partially Asymmetric Exclusion Processes with Sitewise Disorder

We study the stationary properties as well as the non-stationary dynamics of the one-dimensional partially asymmetric exclusion process with position dependent random hop rates. In a finite system of $L$ sites the stationary current, $J$, is determined by the largest barrier and the corresponding waiting time, $τ\sim J^{-1}$, is related to the waiting time of a single random walker, $τ_{rw}$, as $τ\sim τ_{rw}^{1/2}$. The current is found to vanish as: $J \sim L^{-z/2}$, where $z$ is the dynamical exponent of the biased single particle Sinai walk. Typical stationary states are phase separated: At the largest barrier almost all particles queue at one side and almost all holes are at the other side. The high-density (low-density) region, is divided into $\sim L^{1/2}$ connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study non-stationary processes of the system, like coarsening and invasion. Finally we discuss some related models, where particles of larger size or multiple occupation of lattice sites is considered.

cond-mat.stat-mech↗