Polymer Collapse on Fluctuating Random Surfaces

• Published in: arXiv.org
• Main Author: Dalley, Simon
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.01.1995
• Subjects: Collapse; Partitions (mathematics); Scaling laws; Variation
• ISSN: 2331-8422

The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact interactions of relative strength \(1/c\), \(0<c<1\), is found as a function of chain length \(L\) and \(c\). The number of configurations \(L^a {\rm e}^{bL}\) as \(L\to \infty\) is determined, showing that a chain undergoes a third-order collapse transition at \(c=\sqrt{2} -1\); the universal scaling laws are found.