In this paper, we study the role of correlations in the energy landscape of a finite random heteropolymer by developing the mapping onto the generalized random energy model (GREM) proposed by Derrida and Gardner [J. Phys. C 19, 2253 (1986)] in the context of spin glasses. After obtaining the joint distribution for energies of pairs of configurations, and by calculating the entropy of the polymer subject to weak and strong topological constraints, the model yields thermodynamic quantities such as ground-state energy, entropy per thermodynamic basin, and glass transition temperature as functions of the polymer length and packing density. These are found to be very close to the uncorrelated landscape or random energy model (REM) estimates. A tricritical point is obtained where behavior of the order parameter q changes from first order with a discrete jump at the transition, to second-order continuous. While the thermodynamic quantities obtained from the free energy are close to the REM values, the Levinthal entropy describing the number of basins which must be searched at the glass transition is significantly modified by correlations. © 1996 The American Physical Society.

• Received 26 December 1995

DOI:https://doi.org/10.1103/PhysRevE.53.6271