1,721,035 research outputs found
General duality for abelian-group-valued statistical- mechanics models
No full textWe introduce a general class of statistical-mechanics models, taking values in an abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of ``variables'' and a set of ``interactions''. Each interaction is associated with a linear combination of variables; these are summarized in a matrix . A Gibbs factor is associated to each variable (one-body term) and to each interaction. Then we introduce a duality transformation for systems in this class. The duality exchanges the abelian group with its dual, the Gibbs factors with their Fourier transforms, and the interactions with the variables. High (low) couplings in the interaction terms are mapped into low (high) couplings in the one-body terms. If the matrix is interpreted as a vector representation of a matroid, duality exchanges the matroid with its dual. We discuss some physical examples. The main idea is to generalize known models up to eventually include randomness into the pattern of interaction. We introduce and study a random Gaussian , a randomPotts-like model, and a random variant of discrete scalar QED. Although the classical procedure \em 'a la Kramers and Wannier does not extend in a natural way to such a wider class of systems, our weaker procedure applies to these models, too. We shortly describe the consequence of duality for each example
Comparing different improvement programs for the N-vector model
No full textWe discuss the connection between various types of improved actions in the context of the two-dimensional sigma-model. We also discuss spectrum-improved actions showing that these actions do not have any improved behaviour. An O(a(2)) on-shell improved action with all couplings defined on a plaquette and satisfying reflection positivity is also explicitly constructed. (C) 1997 Published by Elsevier Science B.V
An exactly solvable random satisfiability problem
No full textWe introduce a new model for the generation of random satisfiability problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt and Zecchina, which is a variant of the famous K-SAT model: it is extended to q-state variables and relates to a different choice of the statistical ensemble.
The model has an exactly solvable statistic: the critical exponents and scaling functions of the SAT/UNSAT transition are calculable at zero temperature, with no need of replicas, also with exact finite-size corrections.
We also introduce an exact duality of the model, and show an analogy of thermodynamic properties with the random energy model of disordered spin system theory. Relations with error correcting codes are also discussed
Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model
No full textWe consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma -model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m alpha approximate to 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2 alpha. less than or similar to x less than or similar to m(-1). We present a detailed discussion of the possible systematic errors
High-accuracy two-loop computation of the critical mass for Wilson fermions
No full textWe test an algebraic algorithm based on the coordinate-space method, evaluating with high accuracy the critical mass for Wilson fermions in lattice QCD at two loops. We test the results by using different types of infrared regularization
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