Critical behavior of the two-dimensional 2A-->3A, 4A--> phi binary system

Finite-scale singularity in the renormalization group flow of a reaction-diffusion system

We study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a different (conjugated) universality class.

Branching and annihilating random walks: exact results at low branching rate

We present some exact results on the behavior of branching and annihilating random walks, both in the directed percolation and parity conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the branching rate around the nontrivial pure annihilation (PA) model, whose correlation and response function we compute exactly. With this, the nonuniversal threshold value for having a phase transition in the simplest system belonging to the directed percolation universality class is found to coincide with previous nonperturbative renormalization group (RG) approximate results. We also show that the parity conserving universality class has an unexpected RG fixed point structure, with a PA fixed point which is unstable in all dimensions of physical interest.

Branching-rate expansion around annihilating random walks

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the directed percolation universality class. Also, we show that the accepted scenario for the appearance of a phase transition in the parity conserving universality class must be improved. In order to obtain these results we perform an expansion in the branching rate around pure annihilation, a theory without branching. This expansion is possible because we manage to solve pure annihilation exactly in any dimension.

Percolation transition at growing spatiotemporal fractal patterns in models of mesoscopic neural networks

Spike packet propagation is modeled in mesoscopic-scale networks, composed of locally and recurrently coupled neural pools, and embedded in a two-dimensional lattice. Site dynamics is governed by three key parameters--pool connectedness probability, synaptic strength (following the steady-state distribution of some realizations of spike-timing-dependent plasticity learning rule), and the neuron refractoriness. Formation of spatiotemporal patterns in our model, synfire chains, exhibits critical behavior, with the emerging percolation phase transition controlled by the probability for nonzero synaptic strength value. Applying the finite-size scaling method, we infer the critical probability dependence on synaptic strength and refractoriness and determine the effects of connection topology on the pertaining percolation clusters fractal dimensions. We find that the directed percolation and the pair contact process with diffusion constitute the relevant universality classes of phase transitions observed in a class of mesoscopic-scale network models, which may be related to recently reported data on in vitro cultures.

Cluster mean-field study of the parity-conserving phase transition

The phase transition of the branching and annihilating random walk with even offspring is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing the system to reach zero branching rate a phase transition can be seen for any N < or = 12. Coherent anomaly extrapolations applied for the series of approximations results in nu(perpendicular) = 1.85(3) and beta=0.96(2).

Role of diffusion in branching and annihilation random walk models

Different branching and annihilating random walk models are investigated by the cluster mean-field method and simulations in one and two dimensions. In the case of the A-->2A , 2A--> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by the nonperturbative renormalization group method [Phys. Rev. Lett. 92, 255703 (2004)]]. The same type of survey for the A-->2A , 4A--> 0 model results in a reentrant phase diagram, similar to that of the 2A-->3A , 4A--> 0 model [Phys. Rev. E 69, 036112 (2004)]]. Simulations of the A-->2A , 4A--> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.