Freezing in polyampholyte globules: Influence of the long-range nature of the interaction

In random heteropolymer globules with short-range interactions between the monomers, freezing takes place at the microscopic length scale only, and can be described by a 1-step replica symmetry breaking. The fact that the long-range Coulomb interaction has no intrinsic length scale suggests that freezing in random polyampholyte globules might take place at all length scales, corresponding to an overlap parameter q(x) that increases continuously from zero to its maximum value. Study of the polyampholyte globule within the independent interaction approximation seems to confirm this scenario. However, the independent interaction model has an important deficiency: it cannot account for self-screening, and we show that the model is only reliable at length scales shorter than the self-screening length. Using the more realistic sequence model we prove that in the general case of a random heteropolymer globule containing two types of monomers such that unlike monomers attract each other, freezing at arbitrarily large length scales is not possible. For polyampholyte globules this implies that beyond the self-screening length, the freezing behavior is qualitatively the same as in the case of short-range interactions. We find that if the polyampholyte globule is not maximally compact, the degree of frustration is insufficient to obtain freezing.