Critical Casimir forces between defects in the 2D Ising model

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.

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Cited by in corpus (6)

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• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• Drag Coefficient of a Circular Inclusion in a Near-Critical Binary Fluid Membrane
• Critical Casimir effects in 2D Ising model with curved defect lines
• Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects