The dynamical cluster approximation ~DCA! is modified to include disorder. The DCA incorporates nonlocal corrections to local approximations such as the coherent potential approximation ~CPA! by mapping the lattice problem with disorder, and in the thermodynamic limit, to a self-consistently embedded finite-sized cluster problem. It satisfies all of the characteristics of a successful cluster a...

We present a numerical solution of the parquet approximation, a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare interaction thus producing the simplest approximation that one can perform with the set of equations involved in the formalism. The method is applied to the Hubb...

The contact process (CP) is an irreversible lattice model involving nearest neighbor interactions only [1,2]. This model incorporates spontaneous desorption and nearest-neighbor induced adsorption. This stochastic process can be used to mimic epidemic spread as well as catalytic reactions. This model belongs to a general class of nonequilibrium models exhibiting a continuous phase transition. N...

We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of the selected spins. For the spin–cluster a groundstate is exactly calaculated by using graphtheoretical methods. The other spins remain unchanged. This proce...

Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding (dynamical) mean-field approximation...

In 1983, Felderhof, Ford, and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which relates this macroscopic property with the microscopic characteristics of the system. In this article, we analyze the cluster expansion of Felderhof,...

We provide microscopic diagrammatic derivations of the molecular coherent potential approximation ~MCA! and dynamical cluster approximation ~DCA! and show that both are F derivable. The MCA ~DCA! maps the lattice onto a self-consistently embedded cluster with open ~periodic! boundary conditions, and therefore violates ~preserves! the translational symmetry of the original lattice. As a conseque...

A modification of the variational configuration interaction functional in the first-order interacting space for molecular electronic structure is presented. The modified functional is a fully linked expression that by construction is extensive and invariant to transformations of the underlying orbital basis and is exact for an ensemble of separated two-electron subsystems. In addition, an appro...

We analyze the Lipkin Model in the strong coupling limit using effective operator techniques. We present both analytical and numerical results for low energy effective hamil-tonians. We investigate the reliability of various approximations used to simplify the nuclear many body problem, such as the cluster approximation. We demonstrate, in explicit examples, certain limits to the validity of th...