15,263 research outputs found
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
Influence of competition in minimal systems with discontinuous absorbing phase transitions
Contact processes (CP's) with particle creation requiring a minimal
neighborhood (restrictive or threshold CP's) present a novel sort of
discontinuous absorbing transitions, that revealed itself robust under the
inclusion of different ingredients, such as distinct lattice topologies,
particle annihilations and diffusion. Here, we tackle on the influence of
competition between restrictive and standard dynamics (that describes the usual
CP and a continuous DP transition is presented). Systems have been studied via
mean-field theory (MFT) and numerical simulations. Results show partial
contrast between MFT and numerical results. While the former predicts that
considerable competition rates are required to shift the phase transition, the
latter reveals the change occurs for rather limited (small) fractions. Thus,
unlike previous ingredients (such as diffusion and others), limited competitive
rates suppress the phase coexistence.Comment: 8 pages, 6 figure
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.Comment: accepted for publication in Journal of Statistical Mechanics (2014
Exploiting a semi-analytic approach to study first order phase transitions
In a previous contribution, Phys. Rev. Lett 107, 230601 (2011), we have
proposed a method to treat first order phase transitions at low temperatures.
It describes arbitrary order parameter through an analytical expression ,
which depends on few coefficients. Such coefficients can be calculated by
simulating relatively small systems, hence with a low computational cost. The
method determines the precise location of coexistence lines and arbitrary
response functions (from proper derivatives of ). Here we exploit and extend
the approach, discussing a more general condition for its validity. We show
that in fact it works beyond the low limit, provided the first order phase
transition is strong enough. Thus, can be used even to study athermal
problems, as exemplified for a hard-core lattice gas. We furthermore
demonstrate that other relevant thermodynamic quantities, as entropy and
energy, are also obtained from . To clarify some important mathematical
features of the method, we analyze in details an analytically solvable problem.
Finally, we discuss different representative models, namely, Potts, Bell-Lavis,
and associating gas-lattice, illustrating the procedure broad applicability.Comment: 12 pages, 15 figures, accepted for publication in Journal of Chemical
Physics (2013
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 , 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 's. Therefore
direct, simple (when compared with other well established approaches) and very
precise microcanonical quantities can be obtained from the proposed method
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
Effect of diffusion in one-dimensional discontinuous absorbing phase transitions
It is known that diffusion provokes substantial changes in continuous
absorbing phase transitions. Conversely, its effect on discontinuous
transitions is much less understood. In order to shed light in this direction,
we study the inclusion of diffusion in the simplest one-dimensional model with
a discontinuous absorbing phase transition, namely the long-range contact
process (-CP). Particles interact as in the usual CP, but the
transition rate depends on the length of inactive sites according to , where and are control parameters. In the
absence of diffusion, this system presents both a discontinuous and a
continuous phase transition, depending on the value of . The inclusion
of diffusion in this model has been investigated by numerical simulations and
mean-field calculations. Results show that there exists three distinct regimes.
For sufficiently low and large 's the transition is respectively always
discontinuous or continuous, independently of the strength of the diffusion. On
the other hand, in an intermediate range of 's, the diffusion causes a
suppression of the phase coexistence leading to a continuous transition
belonging to the DP universality class. This set of results does not agree with
mean-field predictions, whose reasons will be discussed further
Entropy production and heat capacity of systems under time-dependent oscillating temperature
Using the stochastic thermodynamics, we determine the entropy production and
the dynamic heat capacity of systems subject to a sinusoidally time dependent
temperature, in which case the systems are permanently out of thermodynamic
equilibrium inducing a continuous generation of entropy. The systems evolve in
time according to a Fokker-Planck or to a Fokker-Planck-Kramers equation.
Solutions of these equations, for the case of harmonic forces, are found
exactly from which the heat flux, the production of entropy and the dynamic
heat capacity are obtained as functions of the frequency of the temperature
modulation. These last two quantities are shown to be related to the real an
imaginary parts of the complex heat capacity.Comment: 7 pages, 4 figure
Temporal disorder does not forbid discontinuous absorbing phase transitions in low dimensional systems
Distinct works have claimed that spatial (quenched) disorder can suppress the
discontinuous absorbing phase transitions. Conversely, the scenario for
temporal disorder for discontinuous absorbing phase transitions is unknown. In
order to shed some light in this direction, we tackle its effect in three
bidimensional examples, presenting undoubtedly discontinuous absorbing phase
transitions. Except in one case (to be explained further), the temporal
disorder is introduced by allowing the control parameter to be time dependent
according to a uniform distribution of mean and width
, in which at the emergence of the phase transition the system transits
between active and absorbing regimes. In contrast to the spatial disorder,
numerical results strongly suggest that temporal disorder does not forbid the
existence of discontinuous transition. All cases are signed by behaviors
similar to their pure (without disorder) counterparts, including bistability
around the coexistence point and common finite size scaling behavior with the
inverse of the system volume, as recently proposed in Phys. Rev. E. {\bf 92},
062126 (2015). We also observe that temporal disorder does not induce temporal
Griffiths phases around phase transitions, at least for .Comment: 8 pages, 10 figure
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.Comment: 14 pages and 4 figures. submited to Physical Review
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