Carlos E. Fiore

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 transition 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.

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 a 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.

Canonical and microcanonical Monte Carlo simulations of lattice-gas mixtures.

We propose strict canonical and microcanonical Monte Carlo algorithms for an arbitrary lattice-gas binary mixture. We deduce formulas that allow us to obtain field quantities over the ensembles in which their conjugate extensive quantities are conserved. As an example, we have considered a lattice-gas mixture that is equivalent to the spin-1 Blume-Emery-Griffiths model [Phys. Rev. A 4, 1071 (1971)]. For a finite system and near a phase coexistence, the field as a function of its extensive conjugate shows a loop that disappears in the thermodynamic limit giving rise to the usual tie line. The first-order phase transition was determined by the use of three criteria.

Partial inertia induces additional phase transition in the majority vote model

Explosive (i.e., discontinuous) transitions have aroused great interest by manifesting in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions, and more recently, the majority-vote model with inertia. In the latter, the model rules are slightly modified by the inclusion of a term depending on the local spin (an inertial term). In such a case, Chen etxa0al. [Phys Rev. E 95, 042304 (2017)2470-004510.1103/PhysRevE.95.042304] have found that relevant inertia changes the nature of the phase transition in complex networks, from continuous to discontinuous. Here we give a further step by embedding inertia only in vertices with degree larger than a threshold value 〈k〉k^{*}, 〈k〉 being the mean system degree and k^{*} the fraction restriction. Our results, from mean-field analysis and extensive numerical simulations, reveal that an explosive transition is presented in both homogeneous and heterogeneous structures for small and intermediate k^{*}s. Otherwise, a large restriction can sustain a discontinuous transition only in the heterogeneous case. This shares some similarities with recent results for the Kuramoto model [Phys. Rev. E 91, 022818 (2015)PLEEE81539-375510.1103/PhysRevE.91.022818]. Surprisingly, intermediate restriction and large inertia are responsible for the emergence of an extra phase, in which the system is partially synchronized and the classification of phase transition depends on the inertia and the lattice topology. In this case, the system exhibits two phase transitions.

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.

Comparing the influence of distinct kinds of temporal disorder in a low-dimensional absorbing transition model

Recently it was stated that temporal disorder constitutes a relevant perturbation in absorbing phase transitions for all dimensions. However, its effect on systems other than the standard contact process (CP), its competition with other ingredients (e.g., particle diffusion), and other kinds of disorder (besides the standard types) are unknown. In order to shed some light on the above-mentioned points, we investigate a variant of the usual CP, namely, the triplet annihilation model, in which the competition between triplet annihilation and single particle diffusion leads to an unusual phase diagram behavior, with reentrant shape and endless activity for sufficiently large diffusion rates. Two kinds of time-dependent disorder have been considered. In the former, it is introduced in the creation-annihilation parameters (as commonly considered in recent studies), whereas in the latter, the diffusion rate D is allowed to be time dependent. In all cases, the disorder follows a uniform distribution with fixed mean and width σ. Two values of σ have been considered in order to exemplify the regime of weaker and stronger temporal disorder strengths. Our results show that in the former approach, the disorder suppresses the reentrant phase diagram with a critical behavior deviating from the directed percolation (DP) universality class in the regime of low diffusion rates, while they strongly suggest that the DP class is recovered for larger hopping rates. An opposite scenario is found in the latter disorder approach, with a substantial increase of reentrant shape and the maximum diffusion, in which the reentrant shape also displays a critical behavior consistent with the DP universality class (in similarity with the pure model). In order to compare with very recent claims, the results from taking a bimodal distribution and critical behavior in the limit of strong disorder are presented. Also, the results derived from the mean-field theory are performed, presenting partial agreement with numerical results. Lastly, a comparison with the diffusive disordered CP is undertaken.

Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.

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 et al (2011 Phys. Rev. E 84 011125) 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 an 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 neighbor sites. Both models are investigated under mean field theory (MFT) and Monte Carlo simulations. In similarity with results by Martins et al, the inclusion of distinct sublattice interactions maintains the occurrence of an asymmetric active phase and re-entrant 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.

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 l particles jump to l 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.

Effects of diffusion in competitive contact processes on bipartite lattices

We investigate the influence of particle diffusion in the two-dimension contact process (CP) with a competitive dynamics in bipartite sublattices, proposed in [Phys. Rev. E 84, 011125 (2011)]. The particle creation depends on its first and second neighbors and the extinction increases according to the local density. In contrast to the standard CP model, mean-field theory and numerical simulations predict three stable phases: inactive (absorbing), active symmetric and active asymmetric, signed by distinct sublattice particle occupations. Our results from MFT and Monte Carlo simulations reveal that low diffusion rates do not destroy sublattice ordering, ensuring the maintenance of the asymmetric phase. On the other hand, for diffusion larger than a threshold value Dc, the sublattice ordering is suppressed and only the usual active (symmetric)-inactive transition is presented. We also show the critical behavior and universality classes are not affected by the diffusion.