413 citations · 846 across the 27 of their papers we have counts for
10 papers · 1 filter
High-temperature cluster expansion for classical and quantum spin lattice systems with multi-body interactions
Nguyen Tong Xuan, Roberto Fernandez
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the us…
Convergence of cluster and virial expansions for repulsive classical gases
Roberto Fernández, Nguyen Tong Xuan
We study the convergence of cluster and virial expansions for systems of particles subject to positive two-body interactions. Our results strengthen and generalize existing lower b…
Partially ordered models
Vincent Deveaux, Roberto Fernandez
We provide a formal definition and study the basic properties of partially ordered chains (POC). These systems were proposed to model textures in image processing and to represent…
On the convergence of cluster expansions for polymer gases
Rodrigo Bissacot, Roberto Fernández, Aldo Procacci
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 subse…
The analyticity region of the hard sphere gas. Improved bounds
Roberto Fernandez, Aldo Procacci, Benedetto Scoppola
We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in dimensions. The estimates are determined by the volume of multidimensional r…
Regions without complex zeros for chromatic polynomials on graphs with bounded degree
Roberto Fernandez, Aldo Procacci
We prove that the chromatic polynomial of a finite graph of maximal degree $\D$ is free of zeros for $\card q\ge C^*(\D)$ with $$ C^*(\D) = \min_{0<x…
Cluster expansion for abstract polymer models. New bounds from an old approach
Roberto Fernandez, Aldo Procacci
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…
Mott transition in lattice boson models
Roberto Fernandez, Juerg Froehlich, Daniel Ueltschi
We use mathematically rigorous perturbation theory to study the transition between the Mott insulator and the conjectured Bose-Einstein condensate in a hard-core Bose-Hubbard model…
Non-Gibbsianness of the invariant measures of non-reversible cellular automata with totally asymmetric noise
Roberto Fernandez, Andre Toom
We present a class of random cellular automata with multiple invariant measures which are all non-Gibbsian. The automata have configuration space {0,1}^{Z^d}, with d > 1, and they…
Effective Hamiltonians and Phase Diagrams for Tight-Binding Models
Nilanjana Datta, Roberto Fernandez, Juerg Froehlich
We present rigorous results for several variants of the Hubbard model in the strong-coupling regime. We establish a mathematically controlled perturbation expansion which shows how…