Hyperuniversality and the renormalization group for finite systems

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Abstract
The structure of finite-size scaling within the framework of the field-theoretic renormalization-group approach is examined. New size-dependent ultraviolet divergences are introduced into the theory. It is shown, nonetheless, that ‘‘two-scale-factor’’ universality reflects itself in the finite-size free energy and produces a scaling form such as that discussed by Privman and Fisher. A consequence is that the singular part of the finite-system free energy at the bulk critical point is universal. Extensions to surface and interfacial free energies, first proposed from the results of Ising simulations, are supported qualitatively.