Field-induced phase transitions in ferro-antiferromagnetic diblock copolymers

We study the equilibrium properties of a model of magnetic diblock copolymer where each monomer is decorated with an Ising-like spin. Spins interact ferromagnetically within each block and antiferromagnetically across blocks, generating frustration between magnetic ordering and spatial organization. By employing a mean-field approach and Monte Carlo simulations for self-avoiding walks on the cubic lattice, we investigate the system's response to an external magnetic field. We discover a rich phase diagram that includes: a swollen phase with both filaments magnetically disordered and spatially extended; a mixed compact phase characterized by a single globule in which the two filaments are strongly intertwined; a segregated compact phase composed of two globular, magnetically ordered, and spatially separated blocks. Furthermore, if the magnitude of the intra-block ferromagnetic interaction differs between the two blocks, we observe a hybrid segregated ("tadpole") phase where one extended block coexists with a collapsed one. Mean-field predictions of the location of the phase boundaries are in quantitative agreement with Monte Carlo results. These findings provide a minimal statistical-mechanical framework for field-controlled self-assembly of tunable patterns by magnetically heterogeneous polymers, which may also serve as a simple platform for future investigations of the coupling between internal epigenetic-like states and chromatin folding.