We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness...

We study the annihilation reaction A+A→0 in a two-dimensional square lattice of width W and an infinite length. The behaviour of the density of particles ρ(t) is analyzed. This system exhibits a crossover time tc between the short-time (two-dimensional) and the long-time (one-dimensional)...

We propose a two-dimensional continuum percolation model in an anisotropic medium, which consists of parallel chains of sites coupled to each other weakly via rare “impurities”. By checking simultaneously two percolations, parallel and perpendicular to the chain direction, we show that while...

The critical properties of the mixed-spin Ising model consisting of spin- 1/2 and 3/2 are investigated in the presence of a bimodal random crystal field by using the effective field theory with correlations. The thermal variations of magnetizations are studied in detail to obtain the phase...

The dependence of the phase diagrams on the random crystal field (RCF) is investigated for the spin-1 Blume–Capel (BC) model on the Bethe lattice. The calculations are carried out in terms of the recursion relations for the coordination number z=4 which corresponds to the square lattice. The...

We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P(Δi) = pδ(Δi −Δ) + (1 − p)δ(Δi). We analyse the effects of randomness on the first-order surfaces of the Δ−T−H phase...

In the presence of quenched random crystal fields, phase transitions in magnetic thin films described by the spin-1 Blume–Capel model have been investigated using effective field theory (EFT). Crystal field disorder has been sampled by introducing dilute and trimodal random crystal fields. For...

The effects of random crystal field on the stationary states of the kinetic spin-1 Blume Capel model are studied using the Glauber-type stochastic dynamics under the time-dependent oscillating field assumption. Our investigation, based on the equilibrium ground state phase diagram, revealed many...

We propose a stochastic model of interactive formation of individual expectations regarding the business climate in an industry. Our model is motivated by a business climate survey conducted since 1960 in Germany by the Ifo-institute (www.ifo.de). In accordance with the data structure of this...

A new type of cluster theory in Ising models with an arbitrary spin S(S12) is presented by the use of the differential operator technique and Ising spin identities. The formulations for evaluating the transition line are derived for the two Ising systems with S=1 and 32 as well as for the spin-S...