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Statistical mechanical methods in particle structure analysis of lattice field theories

II. Scalar and surface models

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Abstract

We illustrate on simple examples a new method to analyze the particle structure of lattice field theories. We prove that the two-point function in Ising and rotator models has an Ornstein-Zernike correction at high temperature. We extend this to Ising models at low temperatures if the lattice dimensiond≧3. We prove that the energy-energy correlation function at high temperatures (for Ising orN=2 rotators) decays according to mean field theory (i.e. with the square of the Ornstein-Zernike correction) ifd≧4. We also study some surface models mimicking the strong-coupling expansion of the glueball correlation function. In the latter model, besides Ornstein-Zernike decay, we establish the presence of two nearly degenerate bound states.

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Authors and Affiliations

  1. Institut de Physique Théorique, Université Catholique de Louvain, B-1348, Louvain-la-Neuve, Belgium

    J. Bricmont

  2. Theoretical Physics, ETH-Hönggerberg, CH-8093, Zürich, Switzerland

    J. Fröhlich

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  1. J. Bricmont
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  2. J. Fröhlich
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Communicated by A. Jaffe

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Bricmont, J., Fröhlich, J. Statistical mechanical methods in particle structure analysis of lattice field theories. Commun.Math. Phys. 98, 553–578 (1985). https://doi.org/10.1007/BF01209330

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