Joseph Rogiers

MEAN FIELD RENORMALIZATION GROUP STUDY OF A MODIFIED ASHKIN-TELLER MODEL

We study the phase diagram of a generalization of the Ashkin-Teller model in two dimensions using the mean-field renormalization group (MFRG) theory. We calculate critical surfaces for this three-parameter Hamiltonian of the model using two different approaches, and we discuss the resulting phase diagram and compare it with the results from the molecular-field approximation.

Effect of Gravity and Confinement on Phase Equilibria

We study a fluid or Ising lattice gas confined between two horizontal walls with separation L, in a gravitational field of strength g. For identical walls (with equal surface fields h1 = hL) the familiar capillary condensation and capillary criticality extend to non-zero g. Finite-size scaling predicts that the locus of criticality shrinks to g = 0 for L → ∞, in the manner g ∝ L-(βδ/ν + 1). For opposing walls (with h1 = - hL) we confirm that the bulk two-phase coexistence is suppressed, for g = 0, to below the wetting temperature Tw. However, for small g the bulk two-phase coexistence extends to higher temperatures that increase extremely rapidly with g, up to a maximum temperature that is shifted from the L = ∞ bulk critical point in the manner Tc, max (L) - Tc (∞) ∝ L-1/ν, conform with finite-size scaling.

Series expansions for a generalized XY hamiltonian

Series expansions are derived for the free energy and the fluctuations of a generalized hamiltonian. These series are analysed in the special case of the XY hamiltonian on an f.c.c. lattice in an external parallel magnetic field. The critical indices seem to be independent of the field.

Higher-order correlations in the two-dimensional ising model

Abstract An exact relation between some expectation values of spin operators on the spin- 1 2 Ising model is proven. From this we derive a set of equations equivalent to those obtained by Lee and Barrie and Fisher. Using the exact two-dimensional results for magnetization and pair correlations we get expressions for some three-, four- and five-correlations. From their irregular behaviour near the critical point we conclude that it is difficult to obtain good quantitative results with cumulant expansions in the vicinity of Tc.

Phase diagram of a modified Ashkin-Teller model

We add a term to the original Ashkin-Teller Hamiltonian in order to reduce the degeneracy. It is shoen that a certain class of terms all lead to the same Hamiltonian. The phase diagram of the isotropic model is discussed in the framework of mean field theory. It exhibits a wealth of critical phenomena.

Phase diagram of the extended Ashkin-Teller model

Abstract Possible generalizations of the Ashkin-Teller model are analysed aiming at reduction of degeneracy of the energy levels. The extended isotropic case is considered in the framework of the molecular field approximation. Assuming six order parameters a three dimensional phase diagram is calculated.

Series expansions for a generalized XY hamiltonian: II. Tricritical behaviour of the Takagi model

Abstract The high-temperature series expansions for the square of the fluctuation in the order parameter, for the specific heat, the concentration and the concentration susceptibility for the Takagi model on an f.c.c. lattice are analysed in the field variables. We obtain for the critical exponent γ = 4 3 and the specific heat is possibly logarithmically divergent. If we take the tricritical point to be determined by γt = 1, the tricritical exponents αt, λt and ωt are found to be consistent with 1 2 .

High temperature series expansion for the spin 12XY-model in a magnetic field

Abstract Series expansions for the partition function and the fluctuation in the long range order parameter are presented for the spin 1 2 XY -model on the f.c.c. lattice with an external magnetic field in the z -direction.

Direct estimates for η from series analysis for several lattice models

High temperature series expansions for susceptibility and second moment of the correlation functions are used to obtain series for the susceptibility in terms of the correlation length. Using standard methods for series analysis we can obtain direct estimates for 2 − η. We have done this for several two- and three-dimensional lattice models with nearest neighbour interactions. For two-dimensional models for which the dimension of the order parameter is greater than one we present the first series estimates for η. Indications that correction terms to the leading singularity are important are given. This method may provide an answer to the problem of hyperscaling.

Critical exponents for the two dimensional spin 12 XY model from a seven spin cell real space renormalization group calculation

In this paper we report on a real space renormalization group calculation for the spin 12 XY model on a triangular lattice using cells of seven spins. We applied a linear transformation and imposed a marginality criterion to find η = 0.26 and v = 2.28. The value of η agrees with the value obtained by Kosterlitz for the planar rotator model (η = 0.25).