Self-tuning phase separation in a model with competing interactions inspired by biological cell polarization

We present a theoretical study of a system with competing short-range ferromagnetic attraction and a long-range antiferromagnetic repulsion, in the presence of a uniform external magnetic field. The interplay between these interactions, at sufficiently low temperature, leads to the self-tuning of the magnetization to a value which triggers phase coexistence, even in the presence of the external field. The investigation of this phenomenon is performed using a Ginzburg-Landau functional in the limit of an infinite number of order parameter components large N model. The scalar version of the model is expected to describe the phase separation taking place on a cell surface when this is immersed in a uniform concentration of chemical stimulant. A phase diagram is obtained as a function of the external field and the intensity of the long-range repulsion. The time evolution of the order parameter and of the structure factor in a relaxation process is studied in different regions of the phase diagram