Al Stella

Bulk, surface and hull fractal dimension of critical Ising clusters in d=2

The authors present accurate numerical calculations of the fractal dimension d and surface dimension ds of the critical Ising cluster, in d=2. The results clearly support the values d=187/96, ds=5/6 which are consistent with Ising clusters being described by tricritical q=1 Potts model exponents. From this, the hull dimension dH of critical Ising clusters is found to be dH=11/8, consistent with numerical work of other authors.

Dynamical renormalisation through classical equations of motion

Classical approximations for critical dynamics are taken as the basis of a new dynamical renormalisation group strategy in real space. The approach is phenomenological and avoids proliferation of interactions, as well as memory effects. For the square and cubic Glauber model, the best determinations of static critical properties come up with values for the dynamic exponent which appear compatible with the most recent estimates by Monte Carlo or series expansion methods.

Influence of the reaction field on the nature of the phase transition in the Potts model

It is shown how Onsagers reaction field may be incorporated in mean-field-like calculations for the q-state Potts model. Its influence on the nature of the phase transition is considered both in a one-site and a two-site cluster approximation. Considerable improvement is obtained for qc(d), the value which separates first- and second-order transitions. The way in which qc(d) is modified when a second-neighbour interaction is added to the ferromagnetic nearest-neighbour one is also studied.

A renormalization group analysis of correlation function series expansions

Abstract A new method, inspired by renormalization group ideas, is proposed for extracting information on critical behaviour from series expansions of correlation functions. For the two-dimensional spin 1 2 XY model, the results suggest the existence of a line of critical points.

Comment on the reliability of a real space renormalization approach to the kinetic Ising model

Abstract A recently proposed Migdal-like dynamical renormalization method, working on the equation of motion for the order parameter, is critically analyzed and shown to yield spurious results, consistent with trivial gaussian behaviour.

Reaction-field calculation for the quantum Potts model

The reaction-field approximation is applied to the d-dimensional q-state quantum Potts model in an external transverse field. With the exception of d<or approximately=3, the tricritical value qc(d), below which the system has a second-order phase transition, decreases with increasing external field strength. From the ground state of the quantum d-dimensional model, an improved value of qc is obtained for the classical model in d+1 dimensions. A direct explanation is also obtained for the expected tricritical point in finite-thickness slabs of cubic ferromagnets (like DyAl2) with a field in the (111) direction.

A unified view on various iterative approaches to the ground-state and finite temperature properties of quantum spin systems

Abstract We show that several iterative techniques, which were proposed for calculating ground-state properties of quantum models, can all be derived as the zero-temperature limit of a real-space quantum renormalization method. As a consequence, all these techniques are systematically improvable by a perturbative approach, and may be extended in a natural way to nonzero temperatures.