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.

Based on quasistationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as response functions, cumulants, and equal area probability distributions all scale with the volume, thus allowing proper estimates for the thermodynamic limit. To illustrate these results, five very distinct lattice models displaying nonequilibrium transitions-to single and infinitely many absorbing states-are investigated. The innate difficulties in analyzing absorbing phase transitions are circumvented through quasistationary simulation methods. Our findings (allied to numerical studies in the literature) strongly point to a unifying discontinuous phase transition scaling behavior for equilibrium and this important class of nonequilibrium systems.

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small T's, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable; an enhanced tempering method, the parallel tempering-accurate for small and intermediate system sizes with rather low computational cost-is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phase density at the coexistence.

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. 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 and thus a discontinuous transition. These findings strongly suggest that the above particle creation requirements constitute a minimum and fundamental mechanism determining the phase coexistence in short-range contact processes.

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Discontinuous transitions have received considerable interest due to the uncovering that many phenomena such as catastrophic changes, epidemic outbreaks and synchronization present a behavior signed by abrupt (macroscopic) changes (instead of smooth ones) as a tuning parameter is changed. However, in different cases there are still scarce microscopic models reproducing such above trademarks. With these ideas in mind, we investigate the key ingredients underpinning the discontinuous transition in one of the simplest systems with up-down Z2 symmetry recently ascertained in [Phys. Rev. E 95, 042304 (2017)]. Such system, in the presence of an extra ingredient-the inertia- has its continuous transition being switched to a discontinuous one in complex networks. We scrutinize the role of three central ingredients: inertia, system degree, and the lattice topology. Our analysis has been carried out for regular lattices and random regular networks with different node degrees (interacting neighborhood) through mean-field theory (MFT) treatment and numerical simulations. Our findings reveal that not only the inertia but also the connectivity constitute essential elements for shifting the phase transition. Astoundingly, they also manifest in low-dimensional regular topologies, exposing a scaling behavior entirely different than those from the complex networks case. Therefore, our findings put on firmer bases the essential issues for the manifestation of discontinuous transitions in such relevant class of systems with Z2 symmetry.

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 Blume-Emery-Griffiths (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 toward 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.

We study the applicability of the parallel tempering (PT) method 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 method for the Blume-Emery-Griffiths model, which displays strong first-order transitions at low temperatures. A precise estimate of coexistence lines is obtained, revealing that the PT method may be a successful tool for the characterization of discontinuous transitions.