Phase Transitions in Multicomponent String Model

TL;DR

This paper introduces an exactly solvable one-dimensional string model with adhesion molecules, revealing phase transitions between low and high sticker concentrations, akin to multicomponent membrane behavior.

Contribution

It presents a novel exactly solvable model capturing phase transitions in multicomponent membrane-like systems with adhesion molecules.

Findings

Identifies continuous and discontinuous phase transitions.

Shows coexistence of different membrane phases.

Provides exact solutions for infinite wall separation case.

Abstract

We propose a one-dimensional model of a string decorated with adhesion molecules (stickers) to mimic multicomponent membranes in restricted geometries. The string is bounded by two parallel walls and it interacts with one of them by short range attractive forces while the stickers are attracted by the other wall. The exact solution of the model in the case of infinite wall separation predicts both continuous and discontinuous transitions between phases characterised by low and high concentration of stickers on the string. Our model exhibits also coexistence of these two phases, similarly to models of multicomponent membranes.