arXiv subjects

Róbert Juhász

Publications and source records attributed to Róbert Juhász.

At least 19 recordsLinked to original sources

arXiv2026

Quantum annealing of the random transverse-field Ising model in one, two, and three dimensions

Quantum annealing must be sufficiently slow to prevent defect formation. We study this problem in the random transverse-field Ising model via the adiabatic theorem to obtain the limiting rate at which defect formation can be avoided. Our approach based on the strong-disorder renormalization group (SDRG) technique views the annealing process as a gradual aggregation of strongly coupled clusters, giving access to the elementary events of error formation. We present a scaling theory of the statistics of these events in general dimensions and confront it to an extensive numerical analysis carried out in one, two, and three dimensions by an efficient implementation of the SDRG method. This approach is also validated by exact diagonalization in one dimension by means of the free-fermion technique. Our results consistently show a logarithmically slow decrease of the error density with the annealing time, characterized by the dimension-dependent critical exponents of the corresponding infinite-disorder fixed point of the model. Furthermore, we provide a map of individual events of potential defect formation in the excitation energy - control parameter plane, which may help in the design of optimal annealing paths.

cond-mat.stat-mech↗

arXiv2026

Slow activity decay in excitable models with discontinuous phase transitions

As a simple model of interacting systems of excitable degrees of freedom, we consider a threshold contact process on various lattices and networks, in which a successful activation event requires the presence of more than one active neighbors. We show by combining numerical simulations and a phenomenological theory that, in the two-phase coexistence region and for a sufficiently low initial activity, a slower-than-exponential temporal decay of the global density emerges, caused by the spontaneous formation of slowly vanishing and non-communicating clusters of activity. This slow-decay phenomenon is found to appear generally for regular lattices and also for finite-dimensional random lattices such as the Voronoi-Delaunay network. However, the slow-decay is impeded by small-world property, as demonstrated by simulations on random-regular networks. In the case of a power-law decay of the order parameter, which is valid among others on two-dimensional regular lattices, our phenomenological theory points out that the decaying state is stable against unbounded nucleation only if the decay exponent exceeds $1/2$. Besides the well-known Griffiths effects of quenched random systems, this slow-decay phenomenon rooted in the threshold condition provides an alternative mechanism of off-critical but scale-free dynamics, occurring also in the absence of disorder.

cond-mat.stat-mech↗

arXiv2025

The effect of dispersal area on the extinction threshold

The survival of populations hinges on their ability to offset local extinctions through new colonizations. The dispersal area ($A$) plays a crucial role in this process, as it determines the probability of finding colonizable vacant sites. We investigated the spatial colonization-extinction dynamics in a lattice model (a contact process), exploring various finite dispersal areas and estimating the extinction threshold $λ_E(A)$. Our results revealed a consistent $λ_E(A)$ relationship, largely independent of lattice geometry (except for the smallest $A$). This $λ_E(A)$ relationship obeyed universal scaling laws within two broad ranges of $A$. The scaling relations suggest considerable selection upon the increase of dispersal area, particularly at low $A$ values. We discuss these findings in the broader context of the evolution of dispersal area.

q-bio.PE↗

arXiv2025

Mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain

Based on the strong-disorder renormalization group method, a microscopic mechanism of defect formation in the quantum annealing of the random transverse-field Ising chain is proposed, which represents the annealing process as a gradual aggregation of strongly coupled spin clusters. The ferromagnetic ground state of clusters is either preserved or get excited in pairwise fusions of clusters, depending on the effective annealing rate of the fusion, the latter events being responsible for the appearance of defects in the final state. A consequence of the theory is that, although the Griffiths-McCoy phases surrounding the critical point are gapless, they are still effectively gapped from the point of view of quantum annealing. Thereby we provide an explanation of the finiteness of gap outside of the critical point, which was implicit in an early approach to the problem by Kibble-Zurek scaling [Dziarmaga, Phys. Rev. B {\bf 74}, 064416 (2006)]. Furthermore, by identifying the accessible excitations, we refine the functional form of the vanishing of the gap at the critical point. The defect density in the final state is found to decrease with the annealing time $τ$, as $n(τ)\sim \ln^{-2}\left(\fracτ{\ln^2τ}\right)$ for large $τ$. In addition to this, our approach gives access also to the density of defects at intermediate times of the annealing process.

cond-mat.stat-mech↗

arXiv2025

Activity propagation with Hebbian learning

We investigate the impact of Hebbian learning on the contact process, a paradigmatic model for infection spreading, which has been also proposed as a simple model to capture the dynamics of inter-regional brain activity propagation as well as population spreading. Each of these contexts calls for an extension of the contact process with local learning. We introduce Hebbian learning as a positive or negative reinforcement of the activation rate between a pair of sites after each successful activation event. Learning can happen either in both directions motivated by social distancing (mutual learning model), or in only one of the directions motivated by brain and population dynamics (source or target learning models). Hebbian learning leads to a rich class of emergent behavior, where local incentives can lead to the opposite global effects. In general, positive reinforcement (increasing activation rates) leads to a loss of the active phase, while negative reinforcement (reducing activation rates) can turn the inactive phase into a globally active phase. In two dimensions and above, the effect of negative reinforcement is twofold: it promotes the spreading of activity, but at the same time gives rise to the appearance of effectively immune regions, entailing the emergence of two distinct critical points. Positive reinforcement can lead to Griffiths effects with non-universal power-law scaling, through the formation of random loops of activity, a manifestation of the ``ant mill" phenomenon.

cond-mat.stat-mech↗

arXiv2024

Finite-size scaling and dynamics in a two-dimensional lattice of identical oscillators with frustrated couplings

A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized states, we study numerically the relaxation properties, as well as properties at the stable fixed point which can also be viewed as a metastable state of the closely related XY spin glass model. According to our results, the order parameter at the stable fixed point shows generally a slow, reciprocal logarithmic convergence to its limiting value with the system size. The infinite-size limit is found to be close to zero for zero-centered Gaussian couplings, whereas, for a binary $\pm 1$ distribution with a sufficiently high concentration of positive couplings, it is significantly above zero. Besides, the relaxation time is found to grow algebraically with the system size. Thus, the order parameter in an infinite system approaches its limiting value inversely proportionally to $\ln t$ at late times $t$, similarly to that found in the model with all-to-all couplings [Daido, Chaos {\bf 28}, 045102 (2018)]. As opposed to the order parameter, the energy of the corresponding XY model is found to converge algebraically to its infinite-size limit.

cond-mat.dis-nn↗

arXiv2023

Renormalization theory of disordered contact processes with heavy-tailed dispersal

Motivated by long-range dispersal in ecological systems, we formulate and apply a general strong-disorder renormalization group (SDRG) framework to describe one-dimensional disordered contact processes with heavy-tailed, such as power law, stretched exponential, and log-normal dispersal kernels, widely used in ecology. The focus is on the close-to-critical scaling of the order parameters, including the commonly used density, as well as the less known persistence, which is non-zero in the inactive phase. Our analytic and numerical results obtained by SDRG schemes at different levels of approximation reveal that the more slowly decaying dispersal kernels lead to more smoothly vanishing densities as the critical point is approached. The persistence, however, shows an opposite tendency: the broadening of the dispersal makes its decline more singular at the critical point, becoming discontinuous for the extreme case of power-law dispersal. The SDRG schemes presented here also describe the quantum phase transition of random transverse-field Ising chains with ferromagnetic long-range interactions, the density corresponding to the magnetization of this model.

cond-mat.stat-mech↗

arXiv2022

Exact bounds on the energy gap of transverse-field Ising chains by mapping to random walks

Based on a relationship with continuous-time random walks discovered by Iglói, Turban, and Rieger [Phys. Rev. E {\bf 59}, 1465 (1999)], we derive exact lower and upper bounds on the lowest energy gap of open transverse-field Ising chains, which are explicit in the parameters and are generally valid for arbitrary sets of possibly random couplings and fields. In the homogeneous chain and in the random chain with uncorrelated parameters, both the lower and upper bounds are found to show the same finite-size scaling in the ferromagnetic phase and at the critical point, demonstrating the ability of these bounds to infer the correct finite-size scaling of the critical gap. Applying the bounds to random transverse-field Ising chains with coupling-field correlations, a model which is relevant for adiabatic quantum computing, the finite-size scaling of the gap is shown to be related to that of sums of independent random variables. We determine the critical dynamical exponent of the model and reveal the existence of logarithmic corrections at special points.

cond-mat.stat-mech↗

arXiv2022

Testing the validity of random-singlet state for long-range hopping models through the scaling of entanglement entropy

We consider a sublattice-symmetric free-fermion model on a one-dimensional lattice with random hopping amplitudes decaying with the distance as $|t_l|\sim l^{-α}$, and address the question how far an analogue of the random-singlet state (RSS) conceived originally for describing the ground state of certain random spin chains is valid for this model. For this purpose, we study the effective central charge characterizing the logarithmic divergence of the entanglement entropy (EE) and the prefactor of the distribution of distances between localization centers on the two sublattices, which must fulfill a consistency relation for a RSS. For $α>1$, we find by exact diagonalization an overall logarithmic divergence of the entanglement entropy with an effective central charge varying with $α$. The large $α$ limit of the effective central charge is found to be different from that of the nearest-neighbor hopping model. The consistency relation of RSS is violated for $α\le 2$, while for $α>2$ it is possibly valid, but this conclusion is hampered by a crossover induced by the short-range fixed point. The EE is also calculated by the strong-disorder renormalization group (SDRG) method numerically. Besides the traditional scheme, we construct and apply a more efficient minimal SDRG scheme having a linear (nearest-neighbor) structure, which turns out to be an accurate approximation of the full SDRG scheme for not too small $α$. The SDRG method is found to provide systematically lower effective central charges than exact diagonalization does, nevertheless it becomes more and more accurate for increasing $α$. Furthermore, as opposed to nearest-neighbor models, it indicates a weak dependence on the disorder distribution.

cond-mat.dis-nn↗

arXiv2021

Corrections to the singlet-length distribution and the entanglement entropy in random singlet phases

We consider random singlet phases of spin-$\frac{1}{2}$, random, antiferromagnetic spin chains, in which the universal leading-order divergence $\frac{\ln 2}{3}\ln\ell$ of the average entanglement entropy of a block of $\ell$ spins, as well as the closely related leading term $\frac{2}{3}l^{-2}$ in the distribution of singlet lengths are well known by the strong-disorder renormalization group (SDRG) method. Here, we address the question of how large the subleading terms of the above quantities are. By an analytical calculation performed along a special SDRG trajectory of the random XX chain, we identify a series of integer powers of $1/l$ in the singlet-length distribution with the subleading term $\frac{4}{3}l^{-3}$. Our numerical SDRG analysis shows that, for the XX fixed point, the subleading term is generally $O(l^{-3})$ with a non-universal coefficient and also reveals terms with half-integer powers: $l^{-7/2}$ and $l^{-5/2}$ for the XX and XXX fixed points, respectively. We also present how the singlet lengths originating in the SDRG approach can be interpreted and calculated in the XX chain from the one-particle states of the equivalent free-fermion model. These results imply that the subleading term next to the logarithmic one in the entanglement entropy is $O(\ell^{-1})$ for the XX fixed point and $O(\ell^{-1/2})$ for the XXX fixed point with non-universal coefficients. For the XX model, where a comparison with exact diagonalization is possible, the order of the subleading term is confirmed but we find that the SDRG fails to provide the correct non-universal coefficient.

cond-mat.dis-nn↗

arXiv2020

Emergence of disconnected clusters in heterogeneous complex systems

Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected. This finding indicates a counter-intuitive organization of dynamical correlations, where functional similarity decouples from physical connectivity. We illustrate the phenomena on the example of the Disordered Contact Process (DCP) of infection spreading in heterogeneous systems. We apply numerical simulations and an asymptotically exact renormalization group technique (SDRG) in 1, 2 and 3 dimensional systems as well as in two-dimensional lattices with long-ranged interactions. We conclude that the critical dynamics is well captured by mostly one, highly correlated, but spatially disconnected cluster. Our findings indicate that at criticality the relevant, simultaneously infected sites typically do not directly interact with each other. Due to the similarity of the SDRG equations, our results hold also for the critical behavior of the disordered quantum Ising model, leading to quantum correlated, yet spatially disconnected, magnetic domains.

cond-mat.dis-nn↗

arXiv2020

Persistence discontinuity in disordered contact processes with long-range interactions

We study the local persistence probability during non-stationary time evolutions in disordered contact processes with long-range interactions by a combination of the strong-disorder renormalization group (SDRG) method, a phenomenological theory of rare regions, and numerical simulations. We find that, for interactions decaying as an inverse power of the distance, the persistence probability tends to a non-zero limit not only in the inactive phase but also in the critical point. Thus, unlike in the contact process with short-range interactions, the persistence in the limit $t\to\infty$ is a discontinuous function of the control parameter. For stretched exponentially decaying interactions, the limiting value of the persistence is found to remain continuous, similar to the model with short-range interactions.

cond-mat.stat-mech↗

arXiv2020

Scaling of local persistence in the disordered contact process

We study the time-dependence of the local persistence probability during a non-stationary time evolution in the disordered contact process in $d=1,2$, and $3$ dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply in the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal, dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dependent local persistences is shown to be characterized by a universal limit distribution of effective persistence exponents. By a phenomenological approach of rare-region effects in the active phase, we obtain a non-universal algebraic decay of the average persistence for $d=1$, and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay holds to be valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time-dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.

cond-mat.stat-mech↗

arXiv2020

Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations

We study the scaling of logarithmic negativity between adjacent subsystems in critical fermion chains with various inhomogeneous modulations through numerically calculating its recently established lower and upper bounds. For random couplings, as well as for a relevant aperiodic modulation of the couplings, which induces an aperiodic singlet state, the bounds are found to increase logarithmically with the subsystem size, and both prefactors agree with the predicted values characterizing the corresponding asymptotic singlet state. For the marginal Fibonacci modulation, the prefactors in front of the logarithm are different for the lower and the upper bound, and vary smoothly with the strength of the modulation. In the delocalized phase of the quasi-periodic Harper model, the scaling of the bounds of the logarithmic negativity as well as that of the entanglement entropy are compatible with the logarithmic scaling of the homogeneous chain. At the localization transition, the scaling of the above entanglement characteristics holds to be logarithmic, but the prefactors are significantly reduced compared to those of the translationally invariant case, roughly by the same factor.

cond-mat.dis-nn↗

arXiv2018

Entanglement Entropy of Disordered Quantum Wire Junctions

We consider different disordered lattice models composed of $M$ linear chains glued together in a star-like manner, and study the scaling of the entanglement between one arm and the rest of the system using a numerical strong-disorder renormalization group method. For all studied models, the random transverse-field Ising model (RTIM), the random XX spin model, and the free-fermion model with random nearest-neighbor hopping terms, the average entanglement entropy is found to increase with the length $L$ of the arms according to the form $S(L)=\frac{c_{\rm eff}}{6}\ln L+const$. For the RTIM and the XX model, the effective central charge $c_{\rm eff}$ is universal with respect to the details of junction, and only depends on the number $M$ of arms. Interestingly, for the RTIM $c_{\rm eff}$ decreases with $M$, whereas for the XX model it increases. For the free-fermion model, $c_{\rm eff}$ depends also on the details of the junction, which is related to the sublattice symmetry of the model. In this case, both increasing and decreasing tendency with $M$ can be realized with appropriate junction geometries.

cond-mat.stat-mech↗

arXiv2017

Entanglement across extended random defects in the XX spin chain

We study the half-chain entanglement entropy in the ground state of the spin-1/2 XX chain across an extended random defect, where the strength of disorder decays with the distance from the interface algebraically as $Δ_l\sim l^{-κ}$. In the whole regime $κ\ge 0$, the average entanglement entropy is found to increase logarithmically with the system size $L$ as $S_L\simeq\frac{c_{\rm eff}(κ)}{6}\ln L+const$, where the effective central charge $c_{\rm eff}(κ)$ depends on $κ$. In the regime $κ<1/2$, where the extended defect is a relevant perturbation, the strong-disorder renormalization group method gives $c_{\rm eff}(κ)=(1-2κ)\ln2$, while, in the regime $κ\ge 1/2$, where the extended defect is irrelevant in the bulk, numerical results indicate a non-zero effective central charge, which increases with $κ$. The variation of $c_{\rm eff}(κ)$ is thus found to be non-monotonic and discontinuous at $κ=1/2$.

cond-mat.dis-nn↗

arXiv2016

Long-range random transverse-field Ising model in three dimensions

We consider the random transverse-field Ising model in $d=3$ dimensions with long-range ferromagnetic interactions which decay as a power $α> d$ with the distance. Using a variant of the strong disorder renormalization group method we study numerically the phase-transition point from the paramagnetic side. The distribution of the (sample dependent) pseudo-critical points is found to scale with $1/\ln L$, $L$ being the linear size of the sample. Similarly, the critical magnetization scales with $(\ln L)^χ/L^d$ and the excitation energy behaves as $L^{-α}$. Using extreme-value statistics we argue that extrapolating from the ferromagnetic side the magnetization approaches a finite limiting value and thus the transition is of mixed-order.

cond-mat.stat-mech↗

arXiv2015

Extinction transition in stochastic population dynamics in a random, convective environment

Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random reproduction rates are systematically greater in one direction than in the opposite one. The spatial disorder turns out to be a relevant perturbation but, according to results of Monte Carlo simulations, the behavior of the model at the extinction transition is different from the (infinite randomness) critical behavior of the disordered, symmetric contact process. Depending on the strength $a$ of the asymmetry, the critical population drifts either with a finite velocity or with an asymptotically vanishing velocity as $x(t)\sim t^{μ(a)}$, where $μ(a)<1$. Dynamical quantities are non-self-averaging at the extinction transition; the survival probability, for instance, shows multiscaling, i.e. it is characterized by a broad spectrum of effective exponents. For a sufficiently weak asymmetry, a Griffiths phase appears below the extinction transition, where the survival probability decays as a non-universal power of the time while, above the transition, another extended phase emerges, where the front of the population advances anomalously with a diffusion exponent continuously varying with the control parameter.

cond-mat.dis-nn↗