We present a study of the two species totally asymmetric diffusion model using the Bethe ansatz. The Hamiltonian has Uq(SU(3)) symmetry. We derive the nested Bethe ansatz equations and obtain the dynamical critical exponent from the finite-size scaling properties of the eigenvalue with the smallest real part. The dynamical critical exponent is 32 which is the exponent corresponding to KPZ growt...

The critical phenomenon of the zero temperature superfluid−Bose-glass phase transition for hard-core bosons on a three-dimensional disordered lattice is studied using a quantum real-space renormalization-group method. The correlation-length exponent ν and the dynamic exponent z are computed. The critical exponent z is found to be 2.5 for compressible states and 1.3 for incompressible states. Th...

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localizat...

We characterize the non-Ohmic portion of the conductivity at temperatures T<1 K in the highly correlated transition metal chalcogenide Ni(S,Se)(2). Pressure tuning of the T = 0 metal-insulator transition reveals the influence of the quantum critical point and permits a direct determination of the dynamical critical exponent z = 2.7(+0.3)(-0.4). Within the framework of finite temperature scaling...

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Within the framework of a simple Rouse-type model we present exact analytical results for dynamical critical behaviour on the sol side of the gelation transition. The stress-relaxation function is shown to exhibit a stretched-exponential longtime decay. The divergence of the static shear viscosity is governed by the critical exponent k = φ − β, where φ is the (first) crossover exponent of rando...

Glossary Cluster Clusters are sets of occupied neighbouring sites. Critical exponents At a critical point or second-order phase transition, many quantities diverge or vanish with a power law of the distance from this critical point; the critical exponent is the exponent for this power law. Fractals Fractals have a mass varying with some power of their linear dimension. The exponent of this powe...

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter u (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for 0 < u < 1 the system is massive, for u = 1 it is massless and conformal invariant. For u > 1 the conformal invariance is broken. The syste...