Randomly interacting estate Potts spins may freeze into a Potts-glass phase in which the Potts symmetry is unbroken, on the average. The mean-field theory of this phase transition is presented. Unlike the spin-glass case, there exist two distinct Potts-glass phases that differ in the nature of the correlations among the many degenerate ground states of the system. For p > 4, the transition from the disordered phase is unusual: The freezing occurs discontinuously but without latent heat. Similar results hold for mean-field quadrupolar-glass models.

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The fluctuating intensity of a chaotic semiconductor laser is used for generating random sequences at rates up to 12.5 Gbits/s. The conversion of the fluctuating intensity to a random bit sequence can be implemented in either software or hardware and the overall rate of generation is much faster than any previously reported random number generator based on a physical mechanism. The generator's simplicity, robustness, and insensitivity to control parameters should enable its application to tasks of secure communication and calculation procedures requiring ultrahigh-speed generation of random bit sequences.

A neural network which is capable of recalling without errors any set of linearly independent patterns is studied. The network is based on a Hamiltonian version of the model of Personnaz et al.The energy of a state of N (+1}neurons is the square of the Euclidean distancein phase spacebetween the state and the linear subspace spanned by the patterns. This energy corresponds to nonlocal updatings of the synapses in the learning mode. Results of the mean-field theory (MFT) of the system as well as computer simulations are presented. The stable and metastable states of the network are studied as a function of "temperature" T and a=p/X, where p is the number of ernbedded patterns. The maximum capacity of the network is a=1. For all a (0&a&1}the embedded patterns are not only locally stable but are global minima of the energy. The patterns appear, as metastable states, below a temperature T =T~(a). The temperature T~(a) decreases to zero as a~1. The spurious states of the network are studied in detail in the case of random uncorrelated patterns. At finite p, they are identical to the mixture states of Hopfield s model. At finite a, a spin-glass phase exists as a metastable state. According to the replica symmetric MFT the spinglass state becomes degenerate with the patterns at a=ag:1 2/~and disappears above it. Possible interpretations of this unusual result are discussed. The average radius of attraction R of the patterns has been determined by computer simulations, for sizes up to N =400. The value of R for 0&a & 1 depends on the details of the dynamics. Results for both parallel and serial dynamics are presented. In both cases R is unity (the largest distance in phase space by. definition} at a~0 and decreases monotonically to zero as a~1. -Contrary to the MFT, simulations have not revealed, so far, any singularity in the properties of the spurious states at an intermediate value of a.