On the critical behavior of the surface tension in a random surface model

Abstract

Abstract We examine the continuity of the surface tension α(p), at the critical point Pc, for the surfaces formed in the random plaquette model on Z3 - of independent plaquettes with density p. It is shown that α(p)⩽| In p|P ∞ 2 (1−p), and α(p)⩽| In p|P ∞ , 1 2 (1−p), where P ∞ (q) is the percolation probability in the dual bond percolation model - of independently occupied bonds with qand P ∞, 1 2 (q) is the percolation probability in the semi-infinite system. Under natural assumptions on the bond-percolation transition, these results strongly indicate that the surface tension vanishes continuously as p↑pc.