Swollen-collapsed transition in random hetero-polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic cha rges interacting with the solvent is introduced, whose continuum counterpar t has been proposed by Garel, Leibler and Orland [7]. The transfer matrix t echnique is used to study various constrained annealed systems which approx imate at various degrees of accuracy the original quenched model. For highl y hydrophobic chains an ordinary theta-point transition is found from a hig h temperature swollen phase to a low temperature compact phase. Depending o n the type of constrained averages, at very low temperatures a swollen phas e or a coexistence between compact and swollen phases are found. The result s are carefully compared with the corresponding ones obtained in the contin uum limit, and various improvements in the original calculations are discus sed.