Critical Casimir forces between defects in the 2D Ising model

TL;DR

This paper derives exact expressions for critical Casimir forces between defects in a 2D Ising model, modeling membrane proteins, and shows these forces follow universal scaling laws relevant to biological membranes near criticality.

Contribution

It provides the first exact derivation of critical Casimir interactions between defects in a 2D Ising system, revealing universal scaling functions applicable to biological membrane models.

Findings

Universal scaling functions for defect interactions derived

Critical Casimir forces follow the same scaling law for all defect types

Relevance to membrane protein interactions near critical points

Abstract

An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.