Abstract
The behavior, near the upper critical dimensiond=4, of finite size properties at bulk criticality forn-vector models is shown to dependqualitatively on the type of boundary condition (bc). Contrary to the more complicated behavior which holds for periodic bc's, there exists an ɛ=4−d expansion for Dirichlet (or free) bc's with only integer powers in ɛ. Several universal finite size amplitude ratios are calculated for systems with Dirichlet bc's and spherical shape. This concerns ratios at bulk criticality as well as ratios related to the crossover into the region above the bulk critical temperature where the bulk correlation length is small compared to the diameter of the system and where the same simple type of ɛ-expansion holds. The general finite size scaling form of the free energy for Dirichlet bc's is compared with conjectures by Privman and Fisher.
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References
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Eisenriegler, E. Finite size critical behavior for Dirichlet boundary conditions. Z. Physik B - Condensed Matter 61, 299–309 (1985). https://doi.org/10.1007/BF01317797
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DOI: https://doi.org/10.1007/BF01317797