Investigating higher-order transitions of a flexible homopolymer with a substrate using the generalized microcanonical inflection-point analysis method

Canonical analysis is an invaluable tool for studying the phase transitions of a given system, but differing response signals make a unique identification of phase transitions very difficult. The generalized microcanonical inflection-point analysis method uses minimally sensitive inflection-points of the microcanonical entropy and its derivatives to identify and classify phase transitions to any order for systems of any size. We use this analysis method to investigate higher-order transitions for a coarse-grained flexible homopolymer interacting with an attractive substrate. Our results, obtained from parallel tempering Monte Carlo data, are accumulated in a hyperphase diagram of the inverse microcanonical temperature and surface interaction strength. We find it is necessary to consider higher than second-order transitions to complete transition lines within the diagram. In particular, the adsorption transition order changes from second to third, and eventually fourth order to ensure a complete transition line. We also detect an additional third order transition at a slightly lower temperature which corresponds to a change of structural behavior of the system not clearly signaled in the canonical data.