Partition function zeros and phase transitions for a square-well polymer chain

摘要

The zeros of the canonical partition functions for flexible square-well polymer chains have been approximatelyncomputed for chains up to length 256 for a range of square-well diameters. We have previously shown thatnsuch chain molecules can undergo a coil-globule and globule-crystal transition as well as a direct coil-crystalntransition. Here we show that each of these transitions has a well-defined signature in the complex-plane mapnof the partition function zeros. The freezing transitions are characterized by nearly circular rings of uniformlynspaced roots, indicative of a discontinuous transition. The collapse transition is signaled by the appearance of annelliptical horseshoe segment of roots that pinches down towards the positive real axis and defines a boundary tona root-free region of the complex plane.With increasing chain length, the root density on the circular ring and innthe space adjacent to the elliptical boundary increases and the leading roots move towards the positive real axis.nFor finite-length chains, transition temperatures can be obtained by locating the intersection of the ellipse and/orncircle of roots with the positive real axis. A finite-size scaling analysis is used to obtain transition temperaturesnin the long-chain (thermodynamic) limit. The collapse transition is characterized by crossover and specific-heatnexponents of φ ≈ 0.76(2) and α ≈ 0.66(2), respectively, consistent with a second-order phase transition.