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Orthogonality between scales and wavelets in a representation for correlation functions. The lattice dipole gas and (∇φ)4 models

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Abstract

Exact formulas for the correlation functions of lattice scalar field models in Zd,d⩾3, such as the dipole gas and anharmonic crystal are derived in terms of the effective action generated aftern applications of the block renormalization group transformation. Utilizing the orthogonality between different momentum scales (relations due to the wavelets implicit in the structure of the block renormalization group transformation), the formulas are quite simple, isolate the dominant term, and, in the thermodynamic andn→∞ limits, reduce the analysis to local estimates of the effective action. Based on a large-small field analysis, the two-point function is determined and it is shown how to extend the results to general correlations. The results proved here show the usefulness of the “orthogonality-of-scales” property for the study of correlation functions.

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Authors and Affiliations

  1. Departamento Fisica-ICEx, Universidade Federal de Minas Gerais, Belo Horizonte MG, Brazil

    Emmanuel Pereira & Michael O'Carroll

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  1. Emmanuel Pereira
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  2. Michael O'Carroll
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Pereira, E., O'Carroll, M. Orthogonality between scales and wavelets in a representation for correlation functions. The lattice dipole gas and (∇φ)4 models. J Stat Phys 73, 695–721 (1993). https://doi.org/10.1007/BF01054346

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  • DOI: https://doi.org/10.1007/BF01054346

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