Glass-like behaviour of a spherical model with oscillatory long-range potential

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Abstract

A one-dimensional spherical model with an oscillatory long-range potential is shown to have zero spontaneous magnetization at all temperatures but to have a transition to a phase in which the pair correlation function possesses oscillatory long-range order with period commensurate with that of the potential. The zero-field susceptibility is shown to be finite and possess a cusp singularity at a finite critical temperature.

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