1977•Journal of Mathematical PhysicsRequires access

Correlation functions in the spherical and mean spherical models

Mark Kac, Colin J. Thompson

Abstract

A transformation is obtained relating spherical and mean and spherical averages. The kernel of the transformation is the probability density of N−1ΣNi=1xi2 in the mean spherical model. The transformation is inverted to obtain a simple method for computing spherical averages from mean spherical averages. Averages in the two ensembles are identical except in zero field below the critical temperature.

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Key concepts: Spherical mean, Spherical model, Mathematics, Mean field theory, Transformation (genetics), Spherical harmonics, Spherical coordinate system, Spherical shell