Critical behaviour of anisotropic spiral self avoiding walks
S. S. Manna · Journal of Physics A Mathematical and General · 1984
The author considers three-choice-spiral and two-choice-spiral self avoiding walks (SAWS) on a square lattice, for which the (anisotropic) constraints are such that for any nth step in the x and -x direction, the (n+1)th step is forbidden to be in the clockwise (or anticlockwise) direction, while for the nth step in the y and -y direction, there may or may not be any special constraints for the next step. In the case of three-choice-spiral SAWS, there is no such constraint (other than self avoiding) while, in the case of two-choice-spiral SAWS, with the nth step in the y and -y directions, the (n+1)th step is forbidden to follow the same direction. From exact enumeration results the author finds a new universality class having gamma =1.58+or-0.05 and nu =0.842+or-0.014 for such SAWS.