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

We examine the continuity of the surface tension α(p), at the critical point P_c, for the surfaces formed in the random plaquette model on Z³ - of independent plaquettes with density p. It is shown that α(p)≤|Inp|P_∞²(1-p), and α(p)≤|Inp|P_∞, 1 2(1-p), where P_∞(q) is the percolation probability in the dual bond percolation model - of independently occupied bonds with qandP_{∞, 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↑p_c.