15060511
Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
The authors study the long-time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural network model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, on varying the asymmetry parameter, k, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to 'complex' temporal behaviour. This transition takes place for the same value kc at which one has a change in behaviour for the mean transient length from a power law in the size of the system (N) to an exponential law in N. The 'complex' behaviour during the transient shows strong analogies with chaotic behaviour: decay of temporal correlations, positive Shannon entropy, nonconstant Renyi entropies of different orders. Moreover the transition is very similar to the intermittent transition in chaotic systems: a scaling law for the Shannon entropy and strong fluctuations of the 'effective Shannon entropy' along the transient, for k>kc.
119852951
On the link between strong and weak coupling expansions for the SU(2) lattice gauge theory
The intermediate region between the strong and weak coupling expansions of SU(2) lattice gauge theory is analyzed by inverting the strong coupling series of the average plaquette energy Ep(J). 
 
Taking into account the weak coupling behaviour too, we get Pade approximants for J(Ep) valid in the whole physical region. The zeros of pJ/pEp are mapped into singularities of Ep(J); they occur for complex values of J and give rise to a peak in the specific heat in fair agreement with the Monte Carlo simulation data. The variable Ep is further used to analyze the strong coupling expansions for the roughening indicator, the string tension and the mass gap.
575888
Fluid random surfaces with extrinsic curvature. II
Abstract We present the results of an extension of our previous work on large-scale simulations of dynamically triangulated toroidal random surfaces embedded in R 3 with extrinsic curvature. We find that the extrinsic-curvature specific heat peak ceases to grow on lattices with more than 576 nodes and that the location of the peak λ c also stabilizes. The evidence for a true crumpling transition is still weak. If we assume it exists we can say that the finite-size scaling exponent α / ηd is very close to zero or negative. On the other hand our new data does rule out the observed peak as being a finite-size artifact of the persistence length becoming comparable to the extent of the lattice.