J. Phys. A: Gen. zyxwvutsr 17 zyxwvutsrq (1984) 2837-2841. Printed in Great Britain zyxwv Caliper diameter of branched polymers V Privmant, F Family$ and A MargolinaD t Baker Laboratory, Comell University, Ithaca, NY 14853, USA t Department of Physics, Emory University, Atlanta, C A 30322, USA 8 Department of Chemical Engineering, Princeton University, Princeton, NJ 83544, USA Received 8 May 1984 Abstract. We report analyses of exact numerical data for the spanning diameter of two- dimensional lattice animals up to size zyxwvu N = 17. Estimates of the exponent zyx Y are consistent with previous studies. The leading correction to scaling has an exponent cr = v which does not result from irrelevant variable effects. Interpretation of this correction as a ‘surface’ term is proposed. The scaling form of the radius of gyration, RN, of N-site lattice animals, which model branched polymers in the dilute limit (Lubensky and Isaacson 1979, Family 1980) is RN~(R~)”2=aNY(1 +bN-’+. . .), as zyxw N+co, (1) (see e.g., Stauffer 1978, Peters er zyxwv a1 1979). The second term in (1) represents the leading correction to scaling. Higher-order terms are usually higher powers of 1/ N. One has e = Yy, (2) where y is the absolute value of the leading irrelevant-variable renormalisation group eigen-exponent. Several recent numerical estimates of Y and zyx 0 in two dimensions (Derrida and DeSeze 1982, Family 1980,1983, Guttmann 1982, Margolina er a1 1984a, b, Parisi and Sourlas 1981, Peters et a1 1979, Privman 1984) can all be plausibly sum- marised by the ranges Y = 0.641 zyxwvu f 0.005 (3) and e = 0.87 * 0.07. (4) A different quantity which measures cluster size is the caliper or spanning diameter, (DN), averaged over all N-site animals, defined as a length of a ‘projection’ of an animal on some fixed axis (Quinn et a1 1976, Harrison et al 1978, see also Redner and Yang 1982). One can also define moments (Oh), etc. Asymptotically, for large N, one should have (5) (Oh) = consfant - Rh, k = 1,2, . . . (see, e.g., Harrison et a1 1978), however, new corrections to scaling may be present in (0:). This property has been noticed by Margolina et al (1984a) who studied directed lattice animals. The motivation for studying caliper diameter moments is that there is 0305-4470/84/142837 +05$02.25 zyxwv 0 1984 The Institute of Physics 2837