Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field $D$ for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of $D$.Comment: 11 pages, 2 ps figures include

Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model

A spin-1 model, appropriated to study the competition between bilinear (J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure

Fast Community Identification by Hierarchical Growth

A new method for community identification is proposed which is founded on the analysis of successive neighborhoods, reached through hierarchical growth from a starting vertex, and on the definition of communities as a subgraph whose number of inner connections is larger than outer connections. In order to determine the precision and speed of the method, it is compared with one of the most popular community identification approaches, namely Girvan and Newman's algorithm. Although the hierarchical growth method is not as precise as Girvan and Newman's method, it is potentially faster than most community finding algorithms.Comment: 6 pages, 5 figure

Long-Time Behaviour and Self-Similarity in a Coagulation Equation with Input of Monomers

For a coagulation equation with Becker-Doring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a self-similar function.Comment: 30 pages, 5 Figures, now published in Markov Processes and Related Fields 12, 367-398, (2006