Critical Casimir forces between defects in the 2D Ising model. (7th November 2016)

• Record Type: Journal Article
• Authors: Nowakowski, P; Maciołek, A; Dietrich, S
• Is Part Of: Journal of physics. Volume 49:Number 48(2016)
• Publication Date: 2016-11-07
• Subjects: critical phenomena -- 2D Ising model -- critical Casimir force -- exactly solvable model -- lipid bilayers; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/48/485001
• Languages: English
• ISSNs: 1751-8113

Abstract

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 finite 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.