arXiv subjects

Carlos E. Fiore

Publications and source records attributed to Carlos E. Fiore.

52 records · Page 3Linked to original sources

arXiv2014

Contact processes with competitive dynamics in bipartite lattices: Effects of distinct interactions

The two-dimensional contact process (CP) with a competitive dynamics proposed by Martins {\it et al.} [Phys. Rev. E {\bf 84}, 011125(2011)] leads to the appearance of an unusual active asymmetric phase, in which the system sublattices are unequally populated. It differs from the usual CP only by the fact that particles also interact with their next-nearest neighbor sites via a distinct strength creation rate and for the inclusion of an inhibition effect, proportional to the local density. Aimed at investigating the robustness of such asymmetric phase, in this paper we study the influence of distinct interactions for two bidimensional CPs. In the first model, the interaction between first neighbors requires a minimal neighborhood of adjacent particles for creating new offspring, whereas second neighbors interact as usual (e.g. at least one neighboring particle is required). The second model takes the opposite situation, in which the restrictive dynamics is in the interaction between next-nearest neighbors sites. Both models are investigated under mean field theory (MFT) and Monte Carlo simulations. In similarity with results by Martins {\it et. al.}, the inclusion of distinct sublattice interactions maintain the occurrence of an asymmetric active phase and reentrant transition lines. In contrast, remarkable differences are presented, such as discontinuous phase transitions (even between the active phases), the appearance of tricritical points and the stabilization of active phases under larger values of control parameters. Finally, we have shown that the critical behaviors are not altered due to the change of interactions, in which the absorbing transitions belong to the directed percolation (DP) universality class, whereas second-order active phase transitions belong to the Ising universality class.

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arXiv2014

A minimal mechanism leading to discontinuous phase transitions for short-range systems with absorbing states

Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short range systems with single species, with no extra symmetries or conservation laws. We consider variants of the contact process, in which at least two adjacent particles (instead of one, as commonly assumed) are required to create a new species. Many interaction rules are analyzed, including distinct cluster annihilations and a modified version of the original pair contact process (PCP). Through detailed time dependent numerical simulations we find that for our modified models, the phase transitions are of first-order, hence contrasting with their corresponding usual formulations in the literature, which are of second-order. By calculating the order-parameter distributions, the obtained bimodal shapes as well as the finite scale analysis reinforce coexisting phases, so a discontinuous transition. These findings strongly suggest that above particle creation requirements constitute a minimum and fundamental mechanism determining the phase coexistence in short-range contact processes.

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arXiv2013

Robustness of first-order phase transitions in one-dimensional long-range contact processes

It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link, here we investigate thoroughly a family of long-range contact processes. They are introduced through the transition rate $1+a\ell^{-σ}$, where $\ell$ is the length of inactive islands surrounding particles. In the former approach we reconsider the original model (called $σ-$contact process), by considering distinct mechanisms of weakening the long-range interaction toward the short-range limit. Second, we study the effect of different rules, including creation and annihilation by clusters of particles and distinct versions with infinitely many absorbing states. Our results show that all examples presenting a single absorbing state, a discontinuous transition is possible for small $σ$. On the other hand, the presence of infinite absorbing states leads to distinct scenario depending on the interactions at the frontier of inactive sites.

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arXiv2012

Equivalence between microcanonical methods for lattice models

The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the grand-canonical ensemble. But given that distinct ensembles are equivalent only at the thermodynamic limit, a natural question is if finite size effects would prevent such procedure. In this work we investigate thoroughly this query in different systems yielding first and second order phase transitions. Our study is carried out from the direct comparison with the thermodynamic relation $(\frac{\partial s}{\partial e})$, where the entropy is obtained from the density of states. A systematic analysis for finite sizes is undertaken. We find that, although results become inequivalent for extreme low system sizes, the equivalence holds true for rather small $L$'s. Therefore direct, simple (when compared with other well established approaches) and very precise microcanonical quantities can be obtained from the proposed method.

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arXiv2012

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water, originally proposed by Bell and Lavis. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through orientational order of particles. We have considered the effect of small inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent, by the organization of solvent particles around solute particles, at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum in density (TMD). This coincidence is easily explained for non-interacting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures.

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arXiv2011

Comparing different protocols of temperature selection in the parallel tempering method

Parallel tempering Monte Carlo simulations have been applied to a variety of systems presenting rugged free-energy landscapes. Despite this, its efficiency depends strongly on the temperature set. With this query in mind, we present a comparative study among different temperature selection schemes in three lattice-gas models. We focus our attention in the constant entropy method (CEM), proposed by Sabo {\it et al}. In the CEM, the temperature is chosen by the fixed difference of entropy between adjacent replicas. We consider a method to determine the entropy which avoids numerical integrations of the specific heat and other thermodynamic quantities. Different analyses for first- and second-order phase transitions have been undertaken, revealing that the CEM may be an useful criterion for selecting the temperatures in the parallel tempering

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arXiv2010

A simple protocol for the probability weights of the simulated tempering algorithm: applications to first-order phase transitions

The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights which often demand involving and time consuming calculations. Here it is shown that such weights are quite accurately obtained from the largest eigenvalue of the transfer matrix -- a quantity straightforward to compute from direct Monte Carlo simulations -- thus simplifying the algorithm implementation. As tests, different systems are considered, namely, Ising, Blume-Capel, Blume-Emery-Griffiths and Bell-Lavis liquid water models. In particular, we address first-order phase transition at low temperatures, a regime notoriously difficulty to simulate because the large free-energy barriers. The good results found (when compared with other well established approaches) suggest that the ST can be a valuable tool to address strong first-order phase transitions, a possibility still not well explored in the literature.

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arXiv2010

Comparing parallel and simulated tempering enhanced sampling algorithms at phase transition regimes

Two important enhanced sampling algorithms, simulated (ST) and parallel (PT) tempering, are commonly used when ergodic simulations may be hard to achieve, e.g, due to a phase space separated by large free-energy barriers. This is so for systems around first-order phase transitions, a case still not fully explored with such approaches in the literature. In this contribution we make a comparative study between the PT and ST for the Ising (a lattice-gas in the fluid language) and the BEG (a lattice-gas with vacancies) models at phase transition regimes. We show that although the two methods are equivalent in the limit of sufficiently long simulations, the PT is more advantageous than the ST with respect to all the analysis performed: convergence towards the stationarity; frequency of tunneling between phases at the coexistence; and decay of time-displaced correlation functions of thermodynamic quantities. Qualitative arguments for why one may expect better results from the PT than the ST near phase transitions conditions are also presented.

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arXiv2010

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The Bell-Lavis model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density (TMD). Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded.

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arXiv2009

Liquid polymorphism, order-disorder transitions and anomalous behavior: a Monte Carlo study of the Bell-Lavis model for water

The Bell-Lavis model for liquid water is investigated through numerical simulations. The lattice-gas model on a triangular lattice presents orientational states and is known to present a highly bonded low density phase and a loosely bonded high density phase. We show that the model liquid-liquid transition is continuous, in contradiction with mean-field results on the Husimi cactus and from the cluster variational method. We define an order parameter which allows interpretation of the transition as an order-disorder transition of the bond-network. Our results indicate that the order-disorder transition is in the Ising universality class. Previous proposal of an Ehrenfest second order transition is discarded. A detailed investigation of anomalous properties has also been undertaken. The line of density maxima in the HDL phase is stabilized by fluctuations, absent in the mean-field solution.

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arXiv2008

First-order phase transitions: A study through the parallel tempering method

We study the applicability of the {\it parallel tempering method} (PT) in the investigation of first- order phase transitions. In this method, replicas of the same system are simulated simultaneously at different temperatures and the configurations of two randomly chosen replicas can occasionally be interchanged. We apply the PT for the Blume-Emery-Griffiths (BEG) model, which displays strong first-order transitions at low temperatures. A precise estimate of coexistence lines is obtained, revealing that the PT may be a successful tool for the characterization of discontinuous transitions.

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arXiv2008

Obtaining pressure versus concentration phase diagrams in spin systems from Monte Carlo simulations

We propose an efficient procedure for determining phase diagrams of systems that are described by spin models. It consists of combining cluster algorithms with the method proposed by Sauerwein and de Oliveira where the grand canonical potential is obtained directly from the Monte Carlo simulation, without the necessity of performing numerical integrations. The cluster algorithm presented in this paper eliminates metastability in first order phase transitions allowing us to locate precisely the first-order transitions lines. We also produce a different technique for calculating the thermodynamic limit of quantities such as the magnetization whose infinite volume limit is not straightforward in first order phase transitions. As an application, we study the Andelman model for Langmuir monolayers made of chiral molecules that is equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the phase diagrams in the case where the intermolecular forces favor interactions between enantiomers of the same type (homochiral interactions). In particular, we have determined diagrams in the surface pressure versus concentration plane which are more relevant from the experimental point of view and less usual in numerical studies.

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arXiv2008

Creation-annihilation processes in the ensemble of constant particle number

We study, in the ensemble of constant particle number, processes in which a cluster of particles is annihilated and particles are created catalytically in active sites. In this ensemble, particles belonging to a cluster of $\ell$ particles jump to $\ell$ distinct active sites. As examples of our prescription, we analyze numerically three nonequilibrium systems that annihilate cluster of particles that are identified as conserved versions of the pair annihilation contact model, triplet annihilation contact model and pair contact process. We show also how to set up the constant particle number ensemble from the constant rate ensemble.

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arXiv2008

Phase transition in conservative diffusive contact processes

We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in which the particle number is conserved. The transition between the frozen and active states was determined by studying the system in the subcritical regime and the nature of the transition, whether continuous or first order, was determined by looking at the fractal dimension of the critical cluster. For the single-creation model the transition remains continuous for any diffusion rate. For pair- and triplet-creation models, however, the transition becomes first order for high enough diffusion rate. Our results indicate that in the limit of infinite diffusion rate the jump in density equals 2/3 for the pair-creation model and 5/6 for the triplet-creation model.

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arXiv2008

Contact process with long-range interactions: a study in the ensemble of constant particle number

We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are replaced by an unique process in which a particle of the system chosen at random leaves its place and jumps to an active site. The present approach is particularly useful for determining the transition point and the nature of the transition, whether continuous or discontinuous, by evaluating the fractal dimension of the cluster at the emergence of the phase transition. We also present another criterion appropriate to identify the phase transition that consists of studying the system in the supercritical regime, where the presence of a "loop" characterizes the first-order transition. All results obtained by the present approach are in full agreement with those obtained by using the constant rate ensemble, supporting that, in the thermodynamic limit the results from distinct ensembles are equivalent.

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arXiv2006

Subcritical series expansions for multiple-creation nonequilibrium models

Perturbative subcritical series expansions for the steady properties of a class of one-dimensional nonequilibrium models characterized by multiple-reaction rules are presented here. We developed long series expansions for three nonequilibrium models: the pair-creation contact process, the A-pair-creation contact process, which is closely related system to the previous model, and the triplet-creation contact process. The long series allowed us to obtain accurate estimates for the critical point and critical exponents. Numerical simulations are also performed and compared with the series expansions results.

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