Long-ranged forces due to thermal fluctuations predicted in many correlated fluids in soft matter:
Liquid Crystals, polyelectrolyte solutions, polymer melts, ...
Inclusions on a membrane
Helfrich energy of a membrane with surface tension and bending rigidity:
There is considerable literature on the fluctuation-induced interactions between objects on such membrane:
M. Goulian, R. Bruinsma and P. Pincus, Euro. Phys. Lett. 22, 145 (1993)
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E. Noruzifar, J. Wagner, R. Zandi, Phys. Rev. E 88, 042314 (2013)
General form of the interaction for particles of dimension a has the form:
Composition fluctuations of a membrane
Lipid mixtures composing a membrane can exhibit composition fluctuations, possibly poised close to an Ising critical point.
The resulting fluctuation-induced interactions are determined (at large separation) by appropriate critical exponents:
B.B. Machta, S.L. Veatch, and J.P. Sethna, Phys. Rev. Lett. 109, 138101 (2012) (circles)
O. A. Vasilyev, E. Eisenriegler, and S. Dietrich, Phys. Rev. E 88, 012137 (2013) (needles)
Appealing to conformal invariance at two dimensional criticality, interactions can be computed for arbitrary shapes:
G. Bimonte, T. Emig, and M. Kardar, EuroPhys. Lett. 104, 21001 (2013) (any shape)
The interaction between wedges is set by dimensional arguments, up to an overall coefficient:
For certain critical systems (e.g. the tricritical Ising model), and boundary conditions, it can change sign.
A stable fixed point can be obtained by blunting the wedge at its tip!