Diffraction spectrum of lattice gas models above T_c

TL;DR

This paper studies the diffraction spectra of lattice gas models with ferromagnetic interactions above the critical temperature, demonstrating their almost sure existence, periodicity, and spectral composition.

Contribution

It proves the almost sure existence and detailed spectral structure of diffraction spectra for certain lattice gas models above T_c.

Findings

Diffraction spectra almost surely exist for the models.

Spectra are Z^d-periodic.

Spectra consist of pure point and absolutely continuous parts.

Abstract

The diffraction spectra of lattice gas models on Z^d with finite-range ferromagnetic two-body interaction above T_c or with certain rates of decay of the potential are considered. We show that these diffraction spectra almost surely exist, are Z^d-periodic and consist of a pure point part and an absolutely continuous part with continuous density.