Self-avoiding walk on a three-dimensional Manhattan lattice

We have extended the definition of the Manhattan lattice from two-dimension al to three-dimensional (3D) spaces. The number of self-avoiding walks on t he 3D Manhattan lattice, C-n, and their mean-square end-to-end distances, ( R-n(2)), were counted exactly up to 31 and 30 steps, respectively. Analysis using the method of the Dlog Pode approximant gave the exponents gamma gam ma = 1.1615 +/- 0.0002 and nu = 0.5870 +/- 0.0025, which are in good agreem ent with corresponding values for self-avoiding walks on the ordinary 3D la ttice. This result suggests that self-avoiding walks on the 3D Manhattan la ttice belong to the same universality class as self-avoiding walks on the o rdinary 3D lattice.