Asymptotics of block Toeplitz determinants and the classical dimer model

We compute the asymptotics of a block Toeplitz determinant which arises in the classical dimer model for the triangular lattice when considering the monomer-monomer correlation function. The model depends on a parameter interpolating between the square lattice ($t=0$) and the triangular lattice ($t=1$), and we obtain the asymptotics for $0<t\le 1$. For $0<t<1$ we apply the Szeg\"o Limit Theorem for block Toeplitz determinants. The main difficulty is to evaluate the constant term in the asymptotics, which is generally given only in a rather abstract form

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.

An investigation into the structure and bioavailability of α-tocopherol dispersions in Gelucire 44/14

In this investigation we describe the preparation, physical characterisation and in vivo behaviour of solid dispersions of a liquid nutraceutical, α-tocopherol, in Gelucire 44/14 with a view to establishing whether dispersion in this matrix may provide a means of formulating a liquid drug in a solid dosage form while also improving the oral bioavailability. Using Vitamin E Preparation USP as the source of α-tocopherol, dispersions were prepared using a melt-fusion method with active loadings up to 50% (w/w) and characterised using differential scanning calorimetry and optical microscopy. Capsules containing 300 IU α-tocopherol were manufactured and the absorption profiles compared to a commercial soft gelatin capsule preparation in healthy human volunteers. Confocal laser scanning microscopy (CLSM) studies were performed in order to elucidate the mechanism by which drug release may be occurring. Differential scanning calorimetry studies indicated that the presence of the active had a negligible effect on the melting profile of the carrier, indicating limited miscibility between the two components, a conclusion supported by the microscopy studies. Similarly, the dispersions were shown to exhibit a glass transition corresponding to the incorporated drug, indicating molecular cooperativity and hence phase separation from the lipid base. Despite the phase separation, it was noted that capsules stored for 18 months under ambient conditions showed no evidence of leakage. Bioavailability studies in six healthy male volunteers indicated that the Gelucire 44/14 formulation showed an approximately two-fold increase in total α-tocopherol absorption compared to the commercial preparation. Confocal laser scanning microscopy studies indicated that, on contact with water, the dispersions formed two interfacial layers, from which the Gelucire 44/14 disperses in the liquid medium as small particles. Furthermore, evidence was obtained for the dispersed material becoming incorporated into the hydrated lipid. In conclusion, the dispersion of the liquid drug in Gelucire 44/14 appears to allow the dual advantages of the preparation of a solid formulation and improved bioavailability of this material