Renormalization of the Linked-Cluster Expansion for a Classical Magnet

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Abstract
Classical many-particle systems with nonparticle-like kinematics are considered. The linked-cluster expansion is obtained, and its one- and two-point renormalizations are carried out in complete and direct analogy to the well-known development for the classical gas. In order to make the parallel visible, a set of fictitious one- and two-point potentials are introduced, most of which vanish in the physical domain. The only additional complexity in treating nonparticle-like systems turns out to be an extra set of indices associated with each spatial point. These indices reflect in diagrammatic terms the necessity for labeling each vertex with the number of impinging potential lines. The "accident" which specifically suppresses this index complexity in the case of classical particles is noted. Both functional and diagrammatic methods are employed. Extensions and applications are briefly discussed.