相关论文: Bethe approximation for a system of hard rigid rod…

A long-standing open question is which graph class is the most general one permitting constant-time constant-factor approximations for dominating sets. The approximation ratio has been bounded by increasingly general parameters such as…

Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…

A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity--a strongly coupled regime…

We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e. it is characterized by Poisson instead of GOE statistics. The physical signature of this phase…

The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an…

We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…

A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…

The leading-order electromagnetic and strong isospin-breaking corrections to the ratio of $K_{\mu 2}$ and $\pi_{\mu 2}$ decay rates are evaluated for the first time on the lattice, following a method recently proposed. The lattice results…

Materials featuring touching points, localized states, and flat bands are of great interest in condensed matter and artificial systems due to their implications in topology, quantum geometry, superconductivity, and interactions. In this…

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

We model fermions with an attractive interaction in an optical lattice with a single-band Hubbard model away from half-filling with on-site attraction $U$ and nearest neighbor hopping $t$. Our goal is to understand the crossover from BCS…

In this talk I consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. I report a rigorous proof of…

We consider the lattice dynamics in the harmonic approximation for We consider the lattice dynamics in the harmonic approximation for a simple hypercubic lattice with arbitrary unit cell. The initial data are random according to a…

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice…

We consider some aspects of a standard model employed in studies of many-body localization: interacting spinless fermions with quenched disorder, for non-zero filling fraction, here on $d$-dimensional lattices. The model may be recast as an…

We review the state of the art on the delocalized non-ergodic regime of the Anderson model on Bethe lattices. We also present new results using Belief Propagation, which consists in solving the self-consistent recursion relations for the…

We consider ``lattice glass models'' in which each site can be occupied by at most one particle, and any particle may have at most l occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase…

Quantum $k$-core percolation is the study of quantum transport on $k$-core percolation clusters where each occupied bond must have at least $k$ occupied neighboring bonds. As the bond occupation probability, $p$, is increased from zero to…

We have investigated the non-equilibrium nature of a lattice gas system consisting of a regular lattice of charged particles driven by an external electric field. For a big system, an exact solution cannot be obtained using a master…