Related papers: Cluster expansions, trees, inversions and correlat…
We consider a system of particles confined in a box $\La\subset\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low…
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions.
A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of…
We propose a method based on cluster expansion to study the low activity/high temperature phase of a continuous particle system confined in a finite volume, interacting through a stable and finite range pair potential with negative minimum…
We perform a cluster expansion in the canonical ensemble with periodic boundary conditions, introducing a new choice of polymer activities that differs from the standard ones. This choice leads to an improved bound for the convergence of…
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates…
We consider a binary system of small and large objects in the continuous space interacting via a non-negative potential. By integrating over the small objects, the effective interaction between the large ones becomes multi-body. We prove…
We show the validity of the cluster expansion in the canonical ensemble for the Ising model. We compare the lower bound of its radius of convergence with the one computed by the virial expansion working in the grand-canonical ensemble.…
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…
We consider a classical system of $N$ particles confined in a box $\Lambda\subset\mathbb{R}^d$ interacting via a finite range pair potential. Given the validity of the cluster expansion in the canonical ensemble we compute the error between…
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 bounds on the radii of convergence and on the value of the…
We consider a system of classical particles confined in a box $\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical…
We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…
Influence of surrounding matter on the properties of clusters is considered by an approach combining the methods of statistical and quantum mechanics. A cluster is treated as a bound N-particle system and surrounding matter as thermostat.…
We review the basics of the coupled-cluster expansion formalism for numerical solutions of the many-body problem, and we outline the principles of an approach directed towards an adequate inclusion of continuum effects in the associated…
In this paper, we study thermodynamics of the cluster of galaxies under the effect of dynamical dark energy. We evaluate the configurational integral for interacting system of galaxies in an expanding universe by including the effects…
Nuclear systems are treated within a quantum statistical approach. Correlations and cluster formation are relevant for the properties of warm dense matter, but the description is challenging and different approximations are discussed. The…
Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ 4d gauge theories. The…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…