Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

Oliveira, Marcelo M. de; Luz, M. G. E. da; Fiore, Carlos E.

doi:10.1103/physreve.92.062126

Cited by 31 publications

(54 citation statements)

References 66 publications

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“…To obtain stronger evidence for our view mentioned in this work and deeper insight into the phenomena, further experiments, such as exploring direct visualization of the vortex configuration [52,59], as well as theoretical investigation, may be needed. We believe that the present study will stimulate similar experiments and analysis in other systems where the dynamic ordering and disordering would be observed [10,16,41,48,[60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”

Section: Resultssupporting

confidence: 55%

Competition between dynamic ordering and disordering for vortices driven by superimposed ac and dc forces

et al. 2019

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When a small periodic shear is applied to randomly distributed vortices, they progressively transform into an organized configuration, which is called random organization or dynamic ordering. By contrast, when the vortices with a moderately organized configuration are driven by a small dc force over a random substrate, they are gradually pinned by random pinning sites and finally reach disordered plastic flow, which is indicative of dynamic pinning or dynamic disordering. From the time-dependent voltage (i.e. average velocity), we find that random organization caused by the ac drive is suppressed with an increase in the dc drive superimposed with the ac one, and finally vanishes as the dc voltage becomes equal to the amplitude of the ac voltage in the steady state, where the vortices move in the forward direction only. The steady-state vortex configuration formed with the superimposed ac and dc drives is, in general, not uniform microscopically but comprises organized and disordered regions.

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Section: Resultssupporting

confidence: 55%

Competition between dynamic ordering and disordering for vortices driven by superimposed ac and dc forces

et al. 2019

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“…Although the critical exponents for DP phase transitions are well known, no established scaling behavior is known for the discontinuous case. As it will be shown, our methodology clearly distinguishes continuous from discontinuous transitions, reinforcing previous claims about the existence of a common finite-size scaling for the latter case [18,20,21]. This paper is organized as follows: In Sec.…”

Section: Introductionsupporting

confidence: 71%

“…For equilibrium systems, the maximum of χ and other quantities scale with the system volume and its position α L obeys the asymptotic relation α L = α 0 − c/L 2 [24,25], being α 0 the transition point in the thermodynamic limit and c a constant. Recent papers [18,26,20,21] have shown that similar scaling is verified for nonequilibrium phase transitions. Alternatively, the transition point can also be estimated as the value of α L in which the two peaks of the probability distribution have equal weights (area) [26,21].…”

Section: Numerical Resultsmentioning

confidence: 62%

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Influence of competition in minimal systems with discontinuous absorbing phase transitions

Pianegonda

Fiore

2016

Physica A: Statistical Mechanics and its Applications

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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.

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“…Another feature distinguishing them relies that the continuous case presents an algebraic divergence of its order parameter variance χ = N [ m 2 − m 2 ] at the critical point f c [34]. (In simulations of finite systems, we observe a maximum that increases with the system size N ).…”

Section: Numerical Resultsmentioning

confidence: 99%

Partial inertia induces additional phase transition in the majority vote model

2017

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Recently it has been aroused a great interest about explosive (i.e., discontinuous) transitions. They manifest in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions and more recently, in the majority-vote (MV) 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 case, Chen et al. (Phys Rev. E 95, 042304 (2017)) 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, large restriction can sustain a discontinuous transition only in the heterogeneous case. This shares some similarity with recent results for the Kuramoto model (Phys Rev. E 91, 022818 (2015)). 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.

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Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

Cited by 31 publications

References 66 publications

Competition between dynamic ordering and disordering for vortices driven by superimposed ac and dc forces

Competition between dynamic ordering and disordering for vortices driven by superimposed ac and dc forces

Influence of competition in minimal systems with discontinuous absorbing phase transitions

Partial inertia induces additional phase transition in the majority vote model

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