Theta-point universality of polyampholytes with screened interactions

TL;DR

This study uses an efficient algorithm to analyze the universal behavior of neutral polyampholytes with screened interactions at the theta point, revealing universality class consistency with homopolymers in 2D and 3D.

Contribution

It provides the first exact disorder-averaged statistics for neutral polyampholytes with quenched charges on lattices, demonstrating universality at the theta transition.

Findings

Theta transition exponents match homopolymer universality class in 2D.

Classical exponents are recovered in 3D.

Probability of unique ground state folding decreases exponentially with chain length.

Abstract

By an efficient algorithm we evaluate exactly the disorder-averaged statistics of globally neutral self-avoiding chains with quenched random charge $q_i=\pm 1$ in monomer i and nearest neighbor interactions $\propto q_i q_j$ on square (22 monomers) and cubic (16 monomers) lattices. At the theta transition in 2D, radius of gyration, entropic and crossover exponents are well compatible with the universality class of the corresponding transition of homopolymers. Further strong indication of such class comes from direct comparison with the corresponding annealed problem. In 3D classical exponents are recovered. The percentage of charge sequences leading to folding in a unique ground state approaches zero exponentially with the chain length.