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

TL;DR

This paper investigates a theoretical model with competing interactions that self-tunes to induce phase coexistence, providing insights into biological cell polarization and phase separation phenomena.

Contribution

It introduces a large N Ginzburg-Landau model capturing self-tuning phase separation driven by competing interactions, relevant to biological cell surface behavior.

Findings

Phase diagram as a function of external field and long-range repulsion

Self-tuning of magnetization triggers phase coexistence

Time evolution of order parameter and structure factor analyzed

Abstract

We present a theoretical study of a system with competing short-range ferromagnetic attraction and a long-range anti-ferromagnetic 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 function of the external field and the intensity of the long-range repulsion. The time evolution of order parameter and of the structure factor in a relaxation process are studied in different regions of the phase diagram.