Analysis Of Critical Behavior Research Articles

Analysis of critical and post-critical behaviour of non-linear dynamical systems by the normal form method, Part I: Normalization formulae

A method, based on normal form theory, is presented to study the dynamical behaviour of a system in the neighbourhood of a nearly critical equilibrium state associated with a bifurcation condition. Explicit formulae for the normalization procedure are derived. These formulae can be numerically programmed, avoiding usual complicated algebraic calculations and making the method effectively applicable for n-dimensional systems. Rather general bifurcations can be included: e.g., non-linear flutter (Hopf bifurcation), divergence and internal resonance.

Critical behaviour of transport coefficients at a structural-ferromagnetic transition. I. Electrical resistivity of TbZn

The electrical resistivity rho and its temperature derivative d rho /dT of two TbZn monocrystals have been studied over a large temperature range encompassing the Curie temperature (Tc approximately 199.56K) and the spin reorientation temperature (Tr approximately 61.9K). Particular emphasis is put on the critical behaviour analysis. A detailed study shows that a scaling law behaviour characterised by a finite but fairly small critical exponent cannot be experimentally distinguished from a logarithmic dependence above Tc. The cross-over temperature to the mean field behaviour is also pointed out. Outside the critical region, the anomalously large d rho /dT values observed over most of the ferromagnetic range are explained using a mean field model. Finally, the critical behaviour of d rho /dT near Tr is analysed, and the resemblance to the anomaly observed in the specific heat is pointed out.