Abstract
Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U γ (r)=q(r)+γΦ(γr), in the limitγ→0, where the Fourier transform\(\hat \Phi \)(p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.
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Katz, T.M. Spherical models with a Gates-Penrose-type phase transition. J Stat Phys 38, 589–602 (1985). https://doi.org/10.1007/BF01010479
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DOI: https://doi.org/10.1007/BF01010479