MANHATTAN LATTICE THETA-POINT EXPONENTS FROM KINETIC GROWTH WALKS ANDEXACT RESULTS FROM THE NIENHUIS O(N) MODEL

Kinetic growth walks (KGW) on the Manhattan lattice have previously be en shown to be equivalent to the static problem of interacting self-av oiding walks on that lattice at the theta-temperature. Here, we illust rate how a complete set of exponents for the static problem, including the crossover exponent phi and surface exponents at the ordinary and special transition points, may be obtained from simulations of kinetic walks. In the process we find that phi almost-equal-to 0.430 +/- 0.00 6 which encompasses the conjectured value 3/7 almost-equal-to 0.42857 for the theta-point on an isotropic lattice. Our numerics confirm a pr edicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk tran sition. Furthermore, we point out that a recently examined variant of the Nienhuis O(n) model can be mapped onto theta-point walks on the Ma nhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the num erical conjectures.