CORRIGENDUM: Phase transition in the two-dimensional frustrated x-y model: scaling equations
The author establishes scaling equations for the two-dimensional x-y model with weak frustration using the electrostatic analogy of Kosterlitz and Thouless. In the limit of small disorder he finds a shift in the critical temperature Tc(x)-Tc(0)=-(Jx/kB)(2 pi 2- pi /2 ln 2x) and the exponents are unchanged from the pure values.
Non-exponential rate behaviour
Abstract Three of the mechanisms which lead to non-exponential rate behaviour in phase transitions are identified and reviewed in some detail. The first mechanism is related to spatial variations of the order parameter susceptibility. It is shown that the volume averaged rate behaviour of the order parameter is simply the Laplace transform of the probability distribution of the susceptibility. Analytical solutions for Gaussian, Maxwellian and power-law probabilities are derived. The second mechanism is based on the intrinsic non-linearity of the kinetic driving force. A general time dependent Landau-Ginzburg rate equation is reduced to the Extended Fisher-Kolmogorov (EFK) equation. It is shown that oscillatory front propagation occurs for a large range of physically meaningful model parameters. The rate behaviour depends crucially on the local conservation properties of the order parameter. Non-exponential relaxations and rate behaviour also results from the time evolution of domain patterns. The lateral ...
On the theory of quasi two-dimensional Heisenberg magnets
We investigate theoretically the magnetic properties of a realistic layer type ferromagnet which differs from an isotropic two-dimensional Heisenberg magnet due to small anisotropy and interlayer coupling. An approximation is used which contains the vanishing of long range order and the existence of a Stanley-Kaplan phase transition in the ideal limit. The approach of the ideal limit is studied. Detailed results are presented both in the neighbourhood of the magnetic phase transition and in the low temperature region. The closeness to the isotropic two-dimensional limit has a strong influence on the behaviour in finite magnetic fields for realistic values of anisotropy and interlayer coupling. However, exceedingly small values of these parameters are required to affect the spontaneous magnetization.