Damage spreading for one-dimensional, nonequilibrium models with parity conserving phase transitions

Ódor, Géza; Menyhárd, N.

doi:10.1103/physreve.57.5168

Cited by 15 publications

(21 citation statements)

References 40 publications

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“…Similarly, models with a non-DP transition do not automatically exhibit non-DP damage spreading. For example, Grassbergers cellular automaton A, which has a DP2 phase transition, displays an ordinary DS transition belonging to DP [362].…”

Section: Ds Transitions With Non-dp Behaviormentioning

confidence: 99%

Non-equilibrium critical phenomena and phase transitions into absorbing states

Hinrichsen¹

2000

Advances in Physics

1,621

193

2,266

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This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, fieldtheoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.

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Section: Ds Transitions With Non-dp Behaviormentioning

confidence: 99%

Non-equilibrium critical phenomena and phase transitions into absorbing states

Hinrichsen¹

2000

Advances in Physics

1,621

193

2,266

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“…Thus for the spins the value of the (static) critical exponent β s is zero, in all the three 'directions' of departing from PC (p T , ǫ and h), as mentioned above. (For simulational results see [12,13]).…”

Section: The Nekim Modelmentioning

confidence: 99%

“…In a previous paper of the present authors[13], devoted to damage spreading investigations of different non-equilibrium one-dimensional models, the issue of a CPC transition has already been raised.…”

mentioning

confidence: 99%

Compact parity-conserving percolation in one dimension

Menyhárd

Ódor

1998

J. Phys. A: Math. Gen.

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Compact directed percolation is known to appear at the endpoint of the directed percolation critical line of the Domany-Kinzel cellular automaton in 1 + 1 dimension. Equivalently, such transition occurs at zero temperature in a magnetic field H, upon changing the sign of H, in the one-dimensional Glauber-Ising model, with well-known exponents characterising spin-cluster growth. We have investigated here numerically these exponents in the non-equilibrium generalization (NEKIM) of the Glauber model in the vicinity of the parity-conserving phase transition point of the kinks. Critical fluctuations on the level of kinks are found to affect drastically the characteristic exponents of spreading of spins while the hyperscaling relation holds in its form appropriate for compact clusters.

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“…However this treatment has still not provided theoretical proof for the initial density dependent spreading exponents observed in simulations Jensen and Dickman, 1993a;Mendes et al, 1994;Odor et al, 1998) and by the numerical integration of the Langevin equation (López and Muñoz, 1997). Furthermore the situation is much more complicated when approaching criticality from the inactive phase.…”

Section: E Dp Coupled To Frozen Field Classesmentioning

confidence: 99%

“…For the fermionic AF system mean-field approximations Odor et al, 2002) give a continuous transition with exponents…”

Section: F Dp With Coupled Diffusive Field Classesmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

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Damage spreading for one-dimensional, nonequilibrium models with parity conserving phase transitions

Cited by 15 publications

References 40 publications

Non-equilibrium critical phenomena and phase transitions into absorbing states

Non-equilibrium critical phenomena and phase transitions into absorbing states

Compact parity-conserving percolation in one dimension

Universality classes in nonequilibrium lattice systems

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