We present simulations of 2-d site animals on square and triangular lattices
in non-trivial geomeLattice animals are one of the few critical models in
statistical mechanics violating conformal invariance. We present here
simulations of 2-d site animals on square and triangular lattices in
non-trivial geometries. The simulations are done with the newly developed PERM
algorithm which gives very precise estimates of the partition sum, yielding
precise values for the entropic exponent θ (ZN∼μNN−θ). In particular, we studied animals grafted to the tips of wedges
with a wide range of angles α, to the tips of cones (wedges with the
sides glued together), and to branching points of Riemann surfaces. The latter
can either have k sheets and no boundary, generalizing in this way cones to
angles α>360 degrees, or can have boundaries, generalizing wedges. We
find conformal invariance behavior, θ∼1/α, only for small
angles (α≪2π), while θ≈const−α/2π for
α≫2π. These scalings hold both for wedges and cones. A heuristic
(non-conformal) argument for the behavior at large α is given, and
comparison is made with critical percolation.Comment: 4 pages, includes 3 figure