  Self-avoiding walks self-interacting via nearest neighbours (ISAW) and
self-avoiding trails interacting via multiply-visited sites (ISAT) are two
models of the polymer collapse transition of a polymer in dilute solution. On
the square lattice it has been established numerically that the collapse
transition of each model lies in a different universality class. It has been
shown that by adding stiffness to the ISAW model a second low temperature phase
eventuates and a more complicated phase diagram ensues with three types of
transition that meet at a multi-critical point. For large enough stiffness the
collapse transition becomes first-order. Interestingly, a phase diagram of a
similar structure has been seen to occur in an extended ISAT model on the
triangular lattice without stiffness. It is therefore of interest to see the
effect of adding stiffness to the ISAT model. We have studied by computer
simulation a generalised model of self-interacting self-avoiding trails on the
square lattice with a stiffness parameter added. Intriguingly, we find that
stiffness does not change the order of the collapse transition for ISAT on the
square lattice for a very wide range of stiffness weights. While at the lengths
considered there are clear bimodal distributions for very large stiffness, our
numerical evidence strongly suggests that these are simply finite-size effects
associated with a crossover to a first-order phase transition at infinite
stiffness.
