Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models

TLDR: In this paper, the particle structure of lattice field theories was analyzed and it was shown that the energy-energy correlation function at high temperatures (for Ising or N=2 rotators) decays according to mean field theory (i.e. with the square of the Ornstein-Zernike correction).

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.