Solvable lattice gas models of random heteropolymers at finite density: II. Dynamics and transitions to compact states

In this paper we analyse both the dynamics and the high density physics of the infinite dimensional lattice gas model for random heteropolymers recently introduced in [1]. Restricting ourselves to site-disordered heteropolymers, we derive exact closed deterministic evolution equations for a suitable set of dynamic order parameters (in the thermodynamic limit), and use these to study the dynamics of the system for different choices of the monomer polarity parameters. We also study the equilibrium properties of the system in the high density limit, which leads to a phase diagram exhibiting transitions between swollen states, compact states, and regions with partial compactification. Our results find excellent verification in numerical simulations, and have a natural and appealing interpretation in terms of real heteropolymers.