Abstract
We study random copolymers consisting of two kinds of monomers with attraction between similar kinds. The mean-field analysis of this system indicates a continuous phase transition into a phase with periodic microdomain structure. It is shown that the inverse of the renormalized propagator has a minimum at non-zero wave numbers. Consequently, there is an anomalously large contribution of fluctuations that make the disordered phase locally stable. However, below a certain temperature, the ordered phase is shown to be locally stable and a weak first-order transition is possible, with qualitative differences from the weak crystallization theory developed by Brazovskii. These differences are due to the peculiar form of the fourth-order vertex of the effective Hamiltonian for the system. We calculated the temperature region for the validity of the mean-field estimates of the amplitude and the scale of microphase separation.
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