Lattice trails. II. Numerical results

For pt.I see ibid., vol.18, p.567 (1985). A numerical study of the properties of lattice trails on the honeycomb, square, triangular and simple cubic lattices is made. Critical points are estimated for all lattices, and upper and lower bounds established. Extensive series have been obtained, and series analysis of both trail generating functions and mean square end-to-end distance series are not inconsistent with the conclusion that the problem is in the same universality class as the self-avoiding walk problem. A pseudo star-triangle transformation is defined, and the analyticity properties of that function, coupled with previous exact results, clearly supports that conclusion for the triangular lattice, as well as providing excellent unbiased critical point estimates. The author also shows that the connective constant for d>or=2-dimensional hypercubic trails is strictly greater than the corresponding quantity for SAWs.