Abstract
We have extended the definition of the Manhattan lattice from two-dimensional to three-dimensional (3D) spaces. The number of self-avoiding walks on the 3D Manhattan lattice, Cn, and their mean-square end-to-end distances, ⟨Rn2⟩, were counted exactly up to 31 and 30 steps, respectively. Analysis using the method of the Dlog Padé approximant gave the exponents γ = 1.1615±0.0002 and ν = 0.5870±0.0025, which are in good agreement with corresponding values for self-avoiding walks on the ordinary 3D lattice. This result suggests that self-avoiding walks on the 3D Manhattan lattice belong to the same universality class as self-avoiding walks on the ordinary 3D lattice.