We have seen the Lovász Local Lemma and its stronger variant, Shearer’s Lemma, which is unfortunately quite unwieldy in applications. Quite recently, researchers in mathematical physics discovered an intermediate form of the lemma, which seems to give results close to Shearer’s Lemma but it is much more easily applicable. First let us review a connection between Shearer’s Lemma and statistical ...

We present an approach to the investigation of the statistical properties of weakly coupled map lattices that avoids completely cluster expansion techniques. Although here it is implemented on a simple case we expect similar strategies to be applicable in a much larger class of situations.

We give a new proof of the well-known upper bound on the correlation function of a gas of non-overlapping dipoles of fixed length and discrete orientation working directly in the charge representation, instead of the more usual sine-Gordon representation.

The linked-cluster expansion technique for the high-temperature expansion of spin model is reviewed. A new algorithm for the computation of three-point and higher Green’s functions is presented. Series are computed for all components of two-point Green’s functions for a generalized 3D Ising model, to 25th order on the bcc lattice and to 23rd order on the sc lattice. Series for zero-momentum fou...

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph GT,γ that is constructed from the surface by recursive glueing of elementary pieces that we call tiles. We also give a second formula...

The equilibrium magnetization of concentrated ferrofluids described by a system of polydisperse dipolar hard spheres is calculated as a function of the internal magnetic field using the Born-Mayer or cluster expansion technique. This paper extends the results of Huke and Lücke [Phys. Rev. E 62, 6875 (2000)] obtained for monodisperse ferrofluids. The magnetization is given as a power series expa...

We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability conditions are satisfied. That is, for state space we take a locally compact separable metric space X and a separable metric space S for the mark space. This...

A cluster expansion is introduced for the determination of the optical absorption properties of cluster states in substitutionally disordered molecular crystals. This method is based on the Green’s function expansion in terms of the localized cluster states in the energy region of the guest subband. The general features of the method are illustrated by calculations for a simple two-dimensional ...

The early stage of the ablation plume formation and the following dynamics of the plume expansion are studied numerically using a combination of molecular dynamics and the direct simulation Monte Carlo methods. The direct cluster ejection from the target and the following cluster-monomer and cluster-cluster collisions are considered. The presence of the ablated clusters is shown to strongly aff...

In this study we present the results from realistic N -body modelling of massive star clusters in the Magellanic Clouds. We have computed eight simulations with N ∼ 10 particles; six of these were evolved for at least a Hubble time. The aim of this modelling is to examine in detail the possibility of large-scale core expansion in massive star clusters, and search for a viable dynamical origin f...