Influence of anisotropic next-nearest-neighbor hopping on diagonal charge-striped phases

We consider the model of strongly-correlated system of electrons described by an extended Falicov-Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbor hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbor hopping anisotropy reduces the $\pi/2$-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbor hopping: the stripes are oriented in the direction of the weaker next-nearest-neighbor hopping.Comment: 9 pages, 3 figures, 1 tabl

Ground states and flux configurations of the two dimensional Falicov-Kimball model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an on-site potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles

Cluster expansion for abstract polymer models. New bounds from an old approach

We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach are: (i) a careful consideration of the Penrose identity for truncated functions, and (ii) the use of iterated transformations to bound tree-graph expansions.Comment: 16 pages. This new version, written en reponse to the suggestions of the referees, includes more detailed introductory sections, a proof of the generalized Penrose identity and some additional results that follow from our treatmen

On the convergence of cluster expansions for polymer gases

We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subsets of a countable set (e.g. contour expansions and more generally high- and low-temperature expansions). In order of increasing strength, these criteria are: (i) Dobrushin criterion, obtained by a simple inductive argument; (ii) Gruber-Kunz criterion obtained through the use of Kirkwood-Salzburg equations, and (iii) a criterion obtained by two of us via a direct combinatorial handling of the terms of the expansion. We show that for subset polymers our sharper criterion can be proven both by a suitable adaptation of Dobrushin inductive argument and by an alternative --in fact, more elementary-- handling of the Kirkwood-Salzburg equations. In addition we show that for general abstract polymers this alternative treatment leads to the same convergence region as the inductive Dobrushin argument and, furthermore, to a systematic way to improve bounds on correlations