Lattice polymers with two competing collapse interactions

Abstract

There have been separate studies of the polymer collapse transition, where the collapse was induced by two different types of attraction. In each case, the configurations of the polymer were given by the same subset of random walks being self-avoiding trails on the square lattice. Numerical evidence shows that when interacting via nearest-neighbour contacts, this transition is different from the collapse transition in square-lattice trails interacting via multiply visited sites. While both transitions are second-order, when interacting via nearest-neighbour contacts, the transition is relatively weak with a convergent specific heat, while when interacting via multiply visited sites, the specific heat diverges strongly. Moreover, an estimation of the crossover exponent for the nearest-neighbour contact interaction provides a value close to that of the canonical polymer collapse model of interacting self-avoiding walks, which also interact via nearest-neighbour contacts. From computer simulations using the flatPERM algorithm, we extend these studies by considering a model of self-avoiding trails on the square lattice containing both types of interaction, and which therefore contains all three of the models discussed above as special cases. We find that the strong multiply-visited site collapse is a singular point in the phase diagram and corresponds to a higher order multi-critical point separating a line of weak second-order transitions from a line of first-order transitions.