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Miguel A. Munoz

Publications and source records attributed to Miguel A. Munoz.

At least 55 records · Page 3Linked to original sources
arXiv2003

Mean-field solution of the parity-conserving kinetic phase transition in one dimension

A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class embracing systems that possess two symmetric absorbing states, which in one-dimensional systems, is in many cases equivalent to parity conservation. The phase transition is studied analytically through a mean-field like modification of the so-called {\it parity interval method}. The original method of parity intervals allows for an exact analysis of the diffusion-controlled limit of infinite reaction rate, where there is no active phase and hence no phase transition. For finite rates, we obtain a surprisingly good description of the transition which compares favorably with the outcome of Monte Carlo simulations. This provides one of the first analytical attempts to deal with the broadly studied DP2 universality class.

cond-mat.stat-mech↗
arXiv2003

Stochastic theory of synchronization transitions in extended systems

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits, depending on parameter values, either: i) a continuous transition in the bounded Kardar-Parisi-Zhang universality class, with a zero largest Lyapunov exponent at the critical point; ii) a continuous transition in the directed percolation class, with a negative Lyapunov exponent, or iii) a discontinuous transition (that is argued to be possibly just a transient effect). Cases ii) and iii) exhibit coexistence of synchronized and unsynchronized phases in a broad (fuzzy) region. This phenomenology reproduces almost all the reported features of synchronization transitions of coupled map lattices and other models, providing a unified theoretical framework for the analysis of synchronization transitions in extended systems.

cond-mat.stat-mech↗
arXiv2003

Critical behavior of a bounded Kardar-Parisi-Zhang equation

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which can be classified into universality classes. Here we study in detail one of such classes that can be mapped into a Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative) non-linearity in the presence of a bounding lower (upper) wall. The wall limits the possible values taken by the height variable, introducing a lower (upper) cut-off, and induce a phase transition between a pinned (active) and a depinned (absorbing) phase. This transition is studied here using mean field and field theoretical arguments, as well as from a numerical point of view. Its main properties and critical features, as well as some challenging theoretical difficulties, are reported. The differences with other multiplicative noise and bounded-KPZ universality classes are stressed, and the effects caused by the introduction of ``attractive'' walls, relevant in some physical contexts, are also analyzed.

cond-mat↗
arXiv2002

Some puzzling problems in nonequilibrium field theories

I review some open problems on the ever-growing field of non-equilibrium phase transitions, paying special attention to the formulation of such problems in terms of Langevin equations or, equivalently, field-theoretical descriptions, and their solution using renormalization

cond-mat↗
arXiv2002

Stochastic theory of non-equilibrium wetting

We study a Langevin equation describing non-equilibrium depinning and wetting transitions. Attention is focused on short-ranged attractive substrate-interface potentials. We confirm the existence of first order depinning transitions, in the temperature-chemical potential diagram, and a tricritical point beyond which the transition becomes a non-equilibrium complete wetting transition. The coexistence of pinned and depinned interfaces occurs over a finite area, in line with other non-equilibrium systems that exhibit first order transitions. In addition, we find two types of phase coexistence, one of which is characterized by spatio-temporal intermittency (STI). A finite size analysis of the depinning time is used to characterize the different coexisting regimes. Finally, a stationary distribution of characteristic triangles or facets was shown to be responsible for the structure of the STI phase.

cond-mat↗
arXiv2001

Is the particle current a relevant feature in driven lattice gases?

By performing extensive MonteCarlo simulations we show that the infinitely fast driven lattice gas (IDLG) shares its critical properties with the randomly driven lattice gas (RDLG). All the measured exponents, scaling functions and amplitudes are the same in both cases. This strongly supports the idea that the main relevant non-equilibrium effect in driven lattice gases is the anisotropy (present in both IDLG and RDLG) and not the particle current (present only in the IDLG). This result, at odds with the predictions from the standard theory for the IDLG, supports a recently proposed alternative theory. The case of finite driving fields is also briefly discussed.

cond-mat↗
arXiv2001

Interface depinning versus absorbing-state phase transitions

According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and an order parameter coupled to a non-diffusive conserved field coincide with those of the linear interface depinning model within computational accuracy. In this paper the connection between absorbing state phase transitions and interface pinning in quenched disordered media is investigated. For that, we present a mapping of the interface dynamics in a disordered medium into a Langevin equation for the active-site density and show that a Reggeon-field-theory like description, coupled to an additional non-diffusive conserved field, appears rather naturally. Reciprocally, we construct a mapping from a discrete model belonging in the absorbing state with-a-conserved-field class to a discrete interface equation, and show how a quenched disorder is originated. We discuss the character of the possible noise terms in both representations, and overview the critical exponent relations. Evidence is provided that, at least for dimensions larger that one, both universality classes are just two different representations of the same underlying physics.

cond-mat↗
arXiv2001

Field theory of self-organized fractal etching

We propose a phenomenological field theoretical approach to the chemical etching of a disordered-solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the model evolution, we are able to map the problem into a field theory related to isotropic percolation. To the best of the authors knowledge, it constitutes the first application of field theory to a problem of chemical dynamics. By using this mapping, many of the etching process critical properties are seen to be describable in terms of the percolation renormalization group fixed point. The emerging field theory has the peculiarity of being ``{\it self-organized}'', in the sense that without any parameter fine-tuning, the system develops fractal properties up to certain scale controlled solely by the volume, $V$, of the etching solution. In the limit $V \to \infty$ the upper cut-off goes to infinity and the system becomes scale invariant. We present also a finite size scaling analysis and discuss the relation of this particular etching mechanism with Gradient Percolation. Finally, the possibility of considering this mechanism as a new generic path to self-organized criticality is analyzed, with the characteristics of being closely related to a real physical system and therefore more directly accessible to experiments.

cond-mat↗
arXiv2001

Critical behavior of a one-dimensional fixed-energy stochastic sandpile

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $ζ_c$ of the particle density. Critical exponents are obtained from extensive simulations, which treat both stationary and transient properties. In contrast with other one-dimensional sandpiles, the model appears to exhibit finite-size scaling, though anomalies exist in the scaling of relaxation times and in the approach to the stationary state. The latter appear to depend strongly on the nature of the initial configuration. The critical exponents differ from those expected at a linear interface depinning transition in a medium with point disorder, and from those of directed percolation.

cond-mat.stat-mech↗
arXiv2000

Temporally disordered Ising models

We present a study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations. We reproduce some well known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as for example, globally fluctuating temperatures or random fields). All the predictions coming from our field theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed.

cond-mat↗
arXiv2000

Sandpiles and absorbing-state phase transitions: recent results and open problems

We review some recent results on the relations between sandpiles and a class of absorbing state phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to exhibit an absorbing state transition with critical properties coinciding with those of the corresponding sandpile model. We propose a set of Langevin equations capturing the relevant features of this transition. These equations characterize the universality class of systems with an infinite number of absorbing states and a static conserved field coupled to the order parameter. Different models in this class are identified, and strong evidence is presented showing that the Manna sandpile, as well as some other stochastic sandpiles, belong in this universality class. Finally some open problems and questions are discussed.

cond-mat↗
arXiv2000

Numerical study of persistence in systems with absorbing states

Extensive Monte Carlo simulations are performed in order to evaluate both the local ($θ_{l}$) and global ($θ_{g}$) persistence exponents in the Ziff-Gulari-Barshad (ZGB) (Phy. Rev. Lett. {\bf 56}, 2553, (1986)) irreversible reaction model. In two dimensions and for the second-order irreversible phase transition (IPT) we find, that both the local and the global persistence exhibit power-law behavior with a crossover between two different time regimes. On the other hand, at the first-order IPT, characteristic of the ZGB, active sites are short lived and the persistence decays more abruptly, not being clear whether it shows power law behavior or not. In order to analyze universality issues, we have also studied another model with absorbing states, the contact process, and evaluated the local persistence exponent in dimensions from 1 to 4. A striking apparent {\it super-universality} is reported: the local persistence exponent seems to coincide in both one and two dimensional systems.

cond-mat↗
arXiv2000

Systems with superabsorbing states

We report on some extensive analysis of a recently proposed model [A. Lipowski Phys. Rev. E {\bf 60}, 6255 (1999)] with infinitely many absorbing states. By performing extensive Monte Carlo simulations we have determined critical exponents and show strong evidence that this model is not in the directed percolation universality class. The conjecture that this two-dimensional model exhibits a dimensional reduction (behaving as one-dimensional directed percolation) is firmly disproven. The reason for the model not exhibiting standard directed percolation scaling behavior is traced back to the existence of what we call {\it superabsorbing sites}, i.e. absorbing sites that cannot be directly activated by the presence of neighboring activity in one or more than one directions. Supporting this claim we present two strong evidences: (i) in one dimension, where superabsorbing sites do not appear at the critical point, the system behaves as directed percolation, and (ii) in a modified two-dimensional variation of the model, defined on a honeycomb lattice, for which superabsorbing sites are very rarely observed, directed percolation behavior is recovered. Finally, a parallel updating version of the model exhibiting a nonequilibrium first-order transition is also reported.

cond-mat↗
arXiv2000

Paths to Self-Organized Criticality

We present a pedagogical introduction to self-organized criticality (SOC), unraveling its connections with nonequilibrium phase transitions. There are several paths from a conventional critical point to SOC. They begin with an absorbing-state phase transition (directed percolation is a familiar example), and impose supervision or driving on the system; two commonly used methods are extremal dynamics, and driving at a rate approaching zero. We illustrate this in sandpiles, where SOC is a consequence of slow driving in a system exhibiting an absorbing-state phase transition with a conserved density. Other paths to SOC, in driven interfaces, the Bak-Sneppen model, and self-organized directed percolation, are also examined. We review the status of experimental realizations of SOC in light of these observations.

cond-mat.stat-mech↗
arXiv2000

Interface Scaling in the Contact Process

Scaling properties of an interface representation of the critical contact process are studied in dimensions 1 - 3. Simulations confirm the scaling relation beta_W = 1 - theta between the interface-width growth exponent beta_W and the exponent theta governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-height correlation function shows clear signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett. 83, 4594 (1999)], but no evidence of multiscaling.

cond-mat.stat-mech↗
arXiv2000

Absorbing-state phase transitions in fixed-energy sandpiles

We study sandpile models as closed systems, with conserved energy density $ζ$ playing the role of an external parameter. The critical energy density, $ζ_c$, marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media. Our results strongly suggest that there are at least three distinct universality classes for sandpiles.

cond-mat.stat-mech↗
arXiv1999

Renormalized Field Theory of Infinitely Driven Lattice Gases

We use field theoretic renormalization group methods to study the critical behavior of a recently proposed Langevin equation for driven lattice gases under infinitely fast drive. We perform an expansion around the upper critical dimension, d_c=4, and obtain the critical exponents to one loop order. The main features of the two loop calculation are then outlined. The renormalized theory is shown to exhibit a behavior different from the standard field theory for the DLG, i.e. it is not mean field like.

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