Absorbing-state phase transitions: Exact solutions of small systems

Dickman, Ronald

doi:10.1103/physreve.77.030102

Cited by 5 publications

(12 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although we have shown analytically that an effective temperature and chemical potential cannot be defined in a consistent manner for the KLS model under Metropolis exchange rates, it is interesting to study numerical examples, to assess the degree of inconsistency. We obtain the stationary solution to the master equation for the KLS model, including exchange with a reservoir at temperature T e and chemical potential µ, on a lattice of 4 × 4 sites, using the method of [27]. In the equilibrium case we verify that ∆E = 0 for T e = T n , independent of the exchange rate p r , as expected.…”

Section: A Numerical Examplessupporting

confidence: 55%

Inconsistencies in steady state thermodynamics

Dickman,

Motai

2014

Preprint

Self Cite

View full text Add to dashboard Cite

We address the issue of extending thermodynamics to nonequilibrium steady states. Using driven stochastic lattice gases, we ask whether consistent definitions of an effective chemical potential µ, and an effective temperature T e , are possible. µ and T e are determined via coexistence, i.e., zero flux of particles and energy between the driven system and a reservoir. In the lattice gas with nearest-neighbor exclusion, temperature is not relevant, and we find that the effective chemical potential, a function of density and drive strength, satisfies the zeroth law, and correctly predicts the densities of coexisting systems. In the Katz-Lebowitz-Spohn driven lattice gas both µ and T e need to be defined. We show analytically that in this case the zeroth law is violated for Metropolis exchange rates, and determine the size of the violations numerically. The zeroth law appears to be violated for generic exchange rates. Remarkably, the system-reservoir coupling proposed by Sasa and Tasaki [J. Stat. Phys. 125, 125 (2006)], is free of inconsistencies, and the zeroth law holds. This is because the rate depends only on the state of the donor system, and is independent of that of the acceptor.

show abstract

Section: A Numerical Examplessupporting

confidence: 55%

Inconsistencies in steady state thermodynamics

Dickman,

Motai

2014

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…While somewhat better than the preliminary study of a model in the CDP class, QSA predictions for the SRW model are not of the quality obtained for the contact process [13]. This appears to be connected with the stronger finitesize effects and corrections to scaling observed for models in the CDP class.…”

Section: Discussionmentioning

confidence: 61%

“…In the contact process [13], quantities such as λ S,L andβ(L) vary quite systematically with system size, leading to precise estimates for critical values via BST extrapolation.…”

Section: B Critical Propertiesmentioning

confidence: 99%

“…The former approach furnishes quite accurate predictions for the contact process; a preliminary application to a model in the CDP class yielded less encouraging results, due in part to the small system sizes accessible [13]. The smaller number of configurations (for a given lattice size and particle density) in the SRW model allows us to study somewhat larger systems, leading to improved results in the QS analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

Filho¹,

Dickman²

2011

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32000 sites. The resulting estimates for critical exponents β, β/ν ⊥ , and z, and the moment ratio m 211 = ρ 2 / ρ 2 (ρ is the activity density), based on finite-size scaling at the critical point, are in agreement with previous results for the CDP universality class. We find, however, that the approach to the QS regime is characterized by a different value of the dynamic exponent z than found in the QS regime.

show abstract

“…In the studies reported here we sample the quasistationary (QS) distribution of the process, (that is, conditioned on survival), which has proven a very useful tool in the study of processes with an absorbing state [1,30,31]. For this purpose, we employ a simulation method that yields quasistationary (QS) properties directly, the QS simulation method [32].…”

Section: Model and Methodsmentioning

confidence: 99%

Contact process on a Voronoi triangulation

et al. 2008

Self Cite

View full text Add to dashboard Cite

We study the continuous absorbing-state phase transition in the contact process on the VoronoiDelaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

show abstract

Absorbing-state phase transitions: Exact solutions of small systems

Cited by 5 publications

References 33 publications

Inconsistencies in steady state thermodynamics

Inconsistencies in steady state thermodynamics

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

Contact process on a Voronoi triangulation

Contact Info

Product

Resources

About