Non-perturbative tricritical exponents of trails. II. Exact enumerations on square and simple cubic lattices

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Abstract
For pt.I, see ibid., vol.21, p.773, (1988). The authors present exact enumerations of trails (self-intersecting but non-overlapping lattice walks) tabulated according to their length (l), number of intersection (I) and end-to-end distance for the square lattice (up to l=21, I=7) and for the simple cubic lattice (up to l=15, I=5). They introduce a fugacity for intersection to explore the transition to a collapsed phase through a novel tricritical point which is unaccessible by the renormalisation group approach. The existence of tricritical points in both lattices is manifested by the divergence of the specific heat. The values of the tricritical couplings and exponents are extracted by a DlogPade analysis. They find for the three-dimensional lattice nu t approximately=0.48, and gamma t approximately=0.43 ( nu t approximately=0.52 and gamma t approximately=1.25 for the square lattice).

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