A variational approach to the localization transition of heteropolymers at interfaces

A chain with random hydrophobic-hydrophilic charges is studied in the presence of an interface separating a polar from a non-polar solvent. Within a Gaussian variational approach in replica space, a transition is found, from a high-temperature region, where the chain is delocalized, to a low-temperature region, where the chain is localized at the interface. The transition temperature diverges as the neutrality of the chain is approached. Our results are in agreement with an Imry-Ma type argument by Garel et al. (Europhys. Lett., 8 (1989) 9). The problem of replica symmetry breaking is also addressed, and the replica-symmetric solution is found to be unstable.