Finite-Size and Finite-Temperature Effects in the Conformally Invariant O(N) Vector Model for 2<d<4

Abstract

We study the operator product expansion (OPE) of the auxiliary scalar field \lambda(x) with itself, in the conformally invariant O(N) Vector Model for 2<d<4, to leading order in 1/N in a strip-like geometry with one finite dimension of length L. We show that consistency of the finite-geometry OPE with bulk OPE calculations requires the physical conditions of, either finite-size scaling at criticality, or finite-temperature phase transition.

Comments: 4 pages, 2 eps figures, work presented at the 5th International Workshop on Thermal Field Theories and Their Applications, Regensburg, Germany, August 10-14, 1998