Conformally invariant field theories in two dimensions and corresponding statistical mechanical models

Belavin, Zamlodochikov and Polyakov have recently proposed a class of conformally invariant field theories in two dimension with exactly determined rational critical indices. We establish a tentative identification of a subset of these theories in terms of the O(n) model and theq-state Potts model in 2-dimensions for appropriaten andq. The results of this work were reported in the conference on “Structural Similarities in Exactly Solved Models” at I.T.P. Santa Barbara, August 1984.