[en] We make, on a particular field theory model, an estimate of the weakest long range behaviour necessary to obtain easily a convergent cluster expansion

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[en] Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula. (paper)

[en] Time-dependent Cluster-Variation (TCVM) or path probability (PP) method is based on the principle of minimum free-energy. All the variables at the system occur at t and variation of configurations are determined by path probability parameters at t-Δt. At the equilibrium, most probable path determined from the principle of minimum free-energy. In PP, the important step is determination of weight factor for a path. The Cluster Variation method for the equilibrium cases can be used to find the weight factor. PP method is applied to two energy levels of atom. The probability of being at X₁(t) excited state, X₂(t) ground state is calculated. At the equilibrium case, the ratio of X₁(t) to X₂(t) is found equal to Boltzmann factor (exp(-E/kT)). (author)

[en] The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF

[en] We present a new implementation of the cluster expansion formalism. The new code, UNiversal CLuster Expansion (UNCLE), consolidates recent advances in the methodology and leverages one new development in the formalism itself. As a core goal, the package reduces the need for user intervention, automating the method to reduce human error and judgment. The package extends standard cluster expansion formalism to the more complicated cases of ternary compounds, as well as surfaces, including adsorption and inequivalent sites

[en] In this work we give an algorithm to express as a convergent series the stationary averages for a class of gradient perturbations of a nonsymmetric (nongradient) Ornstein-Uhlenbeck process. The method relies on a cluster expansion in time of the Girsanov-Cameron-Martin formula for the density of the perturbed measure with respect to the Ornstein-Uhlenbeck measure. In the second paper of this series, the approach is extended to more general perturbations

[en] This paper seeks to identify the influence of the activities of the Agrupacion-Cluster de Conocimiento in the improvement of the Intellectual Capital of its partners, especially of their Relational Capital through the generation of inter-organizational spaces for our organizations in the Basque Country. The transmission of this knowledge requires the physical proximity of the people between whom the exchange can to be made. This exchange is facilitated when spaces are created with an atmosphere of total confidence and equality, in which one can express in complete liberty. (Author)

[en] The cluster expansion of the Bernoulli random field percolation probability of the cubic lattice has been built. On its basis, it has been obtained the upper guaranteed estimate of the percolation threshold and corresponding accuracy estimates are proposed when some approximations are built.

[en] An adaptive cluster expansion (CE) method is used to explore surface adsorption and growth processes. Unlike the traditional CE method, suitable effective cluster interaction (ECI) parameters are determined, and then the selected fixed number of ECIs is continually optimized to predict the stable configurations with gradual increase of adatom coverage. Comparing with traditional CE method, the efficiency of the adaptive CE method could be greatly enhanced. As an application, the adsorption and growth of oxygen atoms on one side of pristine graphene was carefully investigated using this method in combination with first-principles calculations. The calculated results successfully uncover the structural evolution of graphene oxide for the different numbers of oxygen adatoms on graphene. The aggregation behavior of the stable configurations for different oxygen adatom coverages is revealed for increasing coverages of oxygen atoms. As a targeted method, adaptive CE can also be applied to understand the evolution of other surface adsorption and growth processes