Nonperturbative tricritical exponents of trails: I. Exact enumeration on a triangular lattice

As the fugacity of intersections in trails (intersecting but non-overlapping lattice walks) is increased, the configurations change from swollen ones, with the scaling exponents of self-avoiding walks, to compact ones. Separating the two regimes is a potentially new tricritical point with no perturbative renormalisation fixed point associated with it. Supporting evidence for the existence of a tricritical point, its likely location and exponents are computed for the first time from exact enumeration of all trails up to length of fifteen lattice constants on the triangular lattice. The divergence of the specific heat indicates the location of the tricritical point. Generalised ratio and Pade methods are used to extract the scaling exponents for the number of configurations and their end-to-end distance.