The mA + nB → Ø diffusion limited reaction with homogeneous initial condition is studied analytically and numerically. Through renormalization group arguments, it is shiown that the system exhibits the anomalous kinetic behavior below the critical dimension dc∗ ≡ 4/(m + n − 1)....

The tensor renormalization group (TRG) is a powerful new approach for coarse-graining classical two-dimensional (2D) lattice Hamiltonians. It uses the intuitive framework of traditional position space renormalization group methods–analyzing flows in the space of Hamiltonian parameters–but...

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method to the one-loop order within the framework of the n-component φ4-model. The finite-size crossover in impure films has been considered on the basis...

A real space renormalization group method is used to study the critical properties of the bond diluted q-state Potts model in the limit q→∞ on a D-dimensional hypercubic lattice. The structure of phase diagram is obtained. The critical exponents and the free energy of the system are obtained...

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently devised a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Levy...

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...

Although much progress has been made in recent years in describing the dynamics of genetic systems, both in population genetics and evolutionary computation, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article, we...

Using a real-space renormalization group procedure with no adjustable parameters, we investigate the Blume-Emery-Griffiths model on the square lattice. The formalism respects sublattice symmetry, allowing the study of both signs of K, the biquadratic exchange coupling. Our results for K 0 are...

Using field-theoretical methods and exploiting conformal invariance, we study Casimir forces at tricritical points exerted by long-range fluctuations of the order-parameter field. Special attention is paid to the situation where the symmetry is broken by the boundary conditions (extraordinary...

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these...