Mapping Self-Organized Criticality onto Criticality

Ising - model description of the SU ( 2 ) 1 quantum critical point in a dimerized two - leg spin - 1 / 2 ladder

A nonperturbative analytical description of the SU(2) 1 quantum critical point in an explicitly dimerized two-leg spin-1/2 Heisenberg ladder is presented. It is shown that this criticality essentially coincides with that emerging in a weakly dimerized spin-1 chain with a small Haldane gap. The approach is based on the mapping onto an SO(3)-symmetric model of three strongly coupled quantum Ising...

On mapping onto self-organized criticality

In the report we have discussed a few aspects of SOC concept which in general have strongly influence on explicitness of mapping process. SOC idea is based on group of models and/does not seem to give quite clear instructions whether mapped phenomena exhibit SOC or not. To present the problem we have performed a computer simulation in order to investigate the effect of the critical point within...

Algorithmic Mapping from Criticality to Self Organized Criticality

Probabilistic cellular automata are prototypes of non equilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany Kinzel model) and the dynamical Ising model. The critical properties of these models are usually obtained by fine-tuning one or more control parameters, as for instance the temperature. We present a method for the parallel evol...

Self-organized criticality in adaptive neural networks

Sandpile Models of Self-Organized Criticality

Self-Organized Criticality is the emergence of long-ranged spatio-temporal correlations in nonequilibrium steady states of slowly driven systems without fine tuning of any control parameter. Sandpiles were proposed as prototypical examples of self-organized criticality. However, only some of the laboratory experiments looking for the evidence of criticality in sandpiles have reported a positive...