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 ...
Critical Properties of Isotropically Interacting Classical Spins Constrained to a Plane
High-temperature expansions of the susceptibility and internal energy (specific heat) are presented for general lattice structure for a system of isotropically interacting unit vectors (or "classical spins") which are constrained to lie in a plane. A phase transition (${T}_{c}g0$) is indicated for two-dimensional lattices; the expected result ${T}_{c}=0$ is found in one dimension, but only upon choosing a more suitable expansion parameter than $\frac{J}{\mathrm{kT}}$. Similarities with the corresponding expansions of the $S=\frac{1}{2}$ Ising and classical Heisenberg models are pointed out; in particular, it is found that certain critical properties of this planar model appear to be bounded on one side by the Ising model and on the other side by the Heisenberg model.