The low–energy excited states of a system of interacting one–dimensional fermions in a conducting state are collective charge and spin density oscillations. The unusual physical properties of such a system (called “Luttinger liquid”) are characterized by the velocities uρ and uσ of the charge and spin excitations, as well as by a parameter Kρ that determines the power law behavior of correlatio...

In this paper we study the representation theory associated to dilute lattice models. Given a solvable lattice model then often there are dilute versions of the model which are also solvable. These dilute models are studied in [Roc92], [GP93], [Gri94] and [WN93]. In this paper we discuss the algebras generated by the single bond transfer matrices and their representation theory. Our motivation ...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple model that (possessing both liquid-crystal and glass transition) unifies different approaches, producing most of the phenomena associated with real glasses, ...

We introduce the asymmetric random cluster (or ARC) model, which is a graphical representation of the Potts lattice gas, and establish its basic properties. The ARC model allows a rich variety of comparisons (in the FKG sense) between models with diierent parameter values; we give, for example, values (; h) for which the 0's connguration in the Potts lattice gas is dominated by the \+" conngura...