Critical behavior of nonequilibrium phase transitions to magnetically ordered states

Birner, Thomas; Lippert, Karen; Müller, Reinhard; Kühnel, A.; Behn, Ulrich

doi:10.1103/physreve.65.046110

Cited by 29 publications

(28 citation statements)

References 24 publications

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“…We summarize and extend the mean-field solution obtained by Birner et al [12] for the MN equation as described in [8,15]:…”

Section: Non Fluctuating Solutionmentioning

confidence: 96%

“…In order to proceed further M is taken equal to its average over realizations, m, which is determined selfconsistently by imposing [9,10,12] …”

Section: Non Fluctuating Solutionmentioning

confidence: 99%

“…Let us now go beyond the results in [12] by computing higher moments m k = φ k = I s,k /I s,0 . The normalization I s,0 scales as m −1−s+ǫ , and to leading order…”

Section: Non Fluctuating Solutionmentioning

confidence: 99%

“…(1) below) were first proposed, to the best of our knowledge, in the context of synchronization of coupled map lattices [7], and soon after studied in Refs. [8,9,10,11,12]. Such equations describe different situations; in particular, there has been a recent interest in their application to non-equilibrium wetting [13] and also to synchronization problems in extended systems [14]; see Ref.…”

Section: Introductionmentioning

confidence: 99%

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Mean-field limit of systems with multiplicative noise

2005

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A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise-intensity (weak, intermediate, and strongnoise) are identified by performing a self-consistent calculation on a fully connected lattice. The most interesting, strong-noise, regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations, as a Ginzburg criterion shows. On the other hand, the self-consistent approach is shown to be valid only in the thermodynamic limit, while for finite systems the critical behavior is found to be different. In this last case, the self-consistent field itself is broadly distributed rather than taking a well defined mean value; its fluctuations, described by an effective zero-dimensional multiplicative noise equation, govern the critical properties. These findings are obtained analytically for a fully connected graph, and verified numerically both on fully connected graphs and on random regular networks. The results presented here shed some doubt on what is the validity and meaning of a standard mean-field approach in systems with multiplicative noise in finite dimensions, where each site does not see an infinite number of neighbors, but a finite one. The implications of all this on the existence of a finite upper critical dimension for multiplicative noise and Kardar-Parisi-Zhang problems are briefly discussed.

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“…We summarize and extend the mean-field solution obtained by Birner et al [12] for the MN equation as described in [8,15]:…”

Section: Non Fluctuating Solutionmentioning

confidence: 96%

“…In order to proceed further M is taken equal to its average over realizations, m, which is determined selfconsistently by imposing [9,10,12] …”

Section: Non Fluctuating Solutionmentioning

confidence: 99%

“…Let us now go beyond the results in [12] by computing higher moments m k = φ k = I s,k /I s,0 . The normalization I s,0 scales as m −1−s+ǫ , and to leading order…”

Section: Non Fluctuating Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mean-field limit of systems with multiplicative noise

2005

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“…Afterward, the value of the nearest-neighbor is substituted by the average field n to obtain a closed Fokker-Planck equation for P (n, t, n ). The steady-state solution is then found from the self-consistency requirement [10] …”

Section: Mean-field Approachmentioning

confidence: 99%

Critical wetting of a class of nonequilibrium interfaces: A mean-field picture

et al. 2007

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A self-consistent mean-field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing Kardar-Parisi-Zhang (KPZ) interfaces in the presence of a bounding substrate. In the case of positive KPZ nonlinearity a single (Gaussian) regime is found. On the contrary, interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order-parameter: (i) a trivial Gaussian regime, (ii) a weak-fluctuation regime with a trivially located critical point and nontrivial exponents, and (iii) a highly non-trivial strong-fluctuation regime, for which we provide a full solution by finding the zeros of paraboliccylinder functions. These analytical results are also verified by solving numerically the self-consistent equation in each case. Analogies with and differences from equilibrium critical wetting as well as nonequilibrium complete wetting are also discussed.

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Linear and Non-linear Fokker–Planck Equations

Frank

2009

Encyclopedia of Complexity and Systems Science

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Critical behavior of nonequilibrium phase transitions to magnetically ordered states

Cited by 29 publications

References 24 publications

Mean-field limit of systems with multiplicative noise

Mean-field limit of systems with multiplicative noise

Critical wetting of a class of nonequilibrium interfaces: A mean-field picture

Linear and Non-linear Fokker–Planck Equations

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