The Six and Eight-Vertex Models Revisited

Elliott Lieb's ice-type models opened up the whole field of solvable models in statistical mechanics. Here we discuss the “commuting transfer matrix” T,Qequations for these models, writing them in a more explicit and transparent notation that we believe offers new insights. The approach manifests the relationship between the six-vertex and chiral Potts models, and between the eight-vertex and Kashiwara–Miwa models.     

Lattice gas generalization of the hard hexagon model. II. The local densities as elliptic functions

In a previous paper we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites. Here we use various mathematical identities (in particular Gordon's generalization of the Rogers-Ramanujan relations) to express the local densities in terms of elliptic functions. The critical behavior is then readily obtained.Supported in part by the National Science Foundation Grant MCS 8201733.     

Study of ferromagnetism–superconductivity interactions in Co/Nb multilayers

We investigate Co/Nb multilayers to explore the spontaneous π-phase shift between the superconducting (SC) layers, which is attributed for causing the non-monotonic change of the SC transition temperature (T_c) with the ferromagnetic (FM) layer thickness (t_FM) in several FM/SC multilayered systems. The issue of interfacial roughness is also explored by growing Co/Nb multilayers at various sputtering pressures. Transport measurements show a non-monotonic dependence of T_c on t_FM, and this dependence is insensitive to the structural variation present in the samples, as measured by X-ray scattering.     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

Free energy of the solvable chiral Potts model

Very recently, it has been shown that there are chiralN-state Potts models in statistical mechanics that satisfy the star-triangle relation. Here it is shown that the relation implies that the free energy (and its derivatives) satisfies certain functional relations. These can be used to obtain the free energy: in particular, we expand about the critical case and find that the exponent is 1–2/N.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Solid-phase synthesis of imidazo[4,5-b]pyridin-2-ones and related urea derivatives by cyclative cleavage of a carbamate linkage

A solid-phase synthesis of substituted cyclic urea derivatives as potential heterocyclic library scaffolds is described. 2-Amino-3-nitropyridine is attached to Wang resin via a carbamate linkage. Reduction of the nitro group was achieved with SnCl(2).2H(2)O. Reductive alkylation with a range of substituted benzaldehydes followed by cyclative cleavage afforded a small library of 3-substituted imidazo[4,5-b]pyridine-2-ones in 33-45% yield and 59-88% purity. Subsequently, this methodology was applied to the synthesis of 3-substituted imidazo[4,5-f]quinolin-2-ones.