1,720,982 research outputs found
Convergent expansions for Random Cluster Model with q > 0 on infinite graphs
No full textIn this paper we extend our previous results on the connectivity functions and pressure of the Random Cluster Model in the highly subcritical phase and in the highly supercritical phase, originally proved only on the cubic lattice Z(d), to a much wider class of infinite graphs. In particular, concerning the subcritical regime, we show that the connectivity functions are analytic and decay exponentially in any bounded degree graph. In the supercritical phase, we are able to prove the analyticity of finite connectivity functions in a smaller class of graphs, namely, bounded degree graphs with the so called minimal cut-set property and satisfying a (very mild) isoperimetric inequality. On the other hand we show that the large distances decay of finite connectivity in the supercritical regime can be polynomially slow depending on the topological structure of the graph. Analogous analyticity results are obtained for the pressure of the Random Cluster Model on an infinite graph, but with the further assumptions of amenability and quasi-transitivity of the graph
Analyticity and mixing properties for random cluster model with q > 0 on Z(d)
No full textWe study the Random Cluster Model on Z(d) supercript stop for p near either 0 or 1 and for all q > 0 and we prove by mean of cluster expansion methods the analyticity of the pressure and finite connectivities in both regimes. These results are valid also in the regime q < 1 and they imply that percolation probability is strictly less than 1
On the Local Central Limit Theorem for Interacting Spin Systems
No full textWe prove the equivalence between integral and local central limit theorem for spin system interacting via an absolutely summable pair potential without any conditions on the temperature of the system
Infinite graphs with a nontrivial bond percolation threshold: Some sufficient conditions
No full textWe consider Bernoulli bond percolation on infinite graphs and we identify a class of graphs for which the critical percolation probability is strictly less than 1. The graphs in this class have to fulfill conditions stated in terms of a minimal cut set property and a logarithmic isoperimetric inequality. For the particular case of planar graphs the condition on minimal cut sets can be be replaced by the assumption that the dual of the graph is bounded degree
Clustering bounds on n-point correlations for unbounded spin systems
No full textWe prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small interaction between sites, large self-interaction, as well as the more delicate small self-interaction or near massive Gaussian regime. A clustering estimate in the latter regime is needed for the Bosonic case of the recent result obtained by Lukkarinen and Spohn on the rigorous control on kinetic scales of quantum fluids
Diffusive-ballistic transition in random walks with long-range self-repulsion
No full textWe prove that a class of random walks on Z(2) with long-range self-repulsive interactions have a diffusive-ballistic phase transition
On Lennard-Jones Type Potentials and Hard-Core Potentials with an Attractive Tail
No full textWe revisit an old tree graph formula, namely the Brydges-Federbush tree identity, and use
it to get new bounds for the convergence radius of the Mayer series for gases of continuous
particles interacting via non absolutely summable pair potentials with an attractive tail
including Lennard-Jones type pair potentials
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
The Blume–Emery–Griffiths Model on the FAD Point and on the AD Line
Full text linkWe analyse the Blume-Emery-Griffiths (BEG) model on the lattice Z(d) on the ferromagnetic-antiquadrupolar-disordered (FAD) point and on the antiquadrupolar-disordered (AD) line. In our analysis on the FAD point, we introduce a Gibbs sampler of the ground states at zero temperature, and we exploit it in two different ways: first, we perform via perfect sampling an empirical evaluation of the spontaneous magnetization at zero temperature, finding a non(z)ero value in d = 3 and a vanishing value in d = 2. Second, using a careful coupling with the Bernoulli site percolation model in d = 2, we prove rigorously that under imposing + boundary conditions, the magnetization in the center of a square box tends to zero in the thermodynamical limit and the two-point correlations decay exponentially. Also, using again a coupling argument, we show that there exists a unique zero-temperature infinite-volume Gibbs measure for the BEG. In our analysis of the AD line we restrict ourselves to d = 2 and, by comparing the BEG model with a Bernoulli site percolation in a matching graph of Z(2), we get a condition for the vanishing of the infinite-volume limit magnetization improving, for low temperatures, earlier results obtained via expansion techniques
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