In this paper we consider a polymer model of self-avoiding trails with both multiply-visited site and nearest-neighbour interactions. This model generalises ISAT and INNSAT. It also contains in a limiting case the ISAW model, when the Boltzmann weight associated with multiply visited sites is sent to zero.
We study the model via computer simulations using the flatPERM algorithm, and so extend the study of INNSAT in \cite{Bedini_2013_INNSAT}. We point out that this model has been studied some time ago by Wu and Bradley \cite{Wu_1990} via real-space renormalisation, which predicted a tetra-critical point separating the ISAT and ISAW collapse points. In contrast, we find that there is likely to be the ISAT collapsed point itself, that separates a line of first-order transitions from ISAW-like weaker \(\theta\)-point type transitions.
In Section \ref{sec:isat-nn} we define the model introduced by Wu and Bradley. In Section \ref{sec:numerical-results}, we present the results of our simulational studies and deduce a conjectured phase diagram. We end by summarising our conclusions in Section \ref{sec:conclusions}.