# Monte Carlo calculation of the critical Casimir force

Presenter: David Lopes Cardozo (Laboratoire de Physique, ENS de Lyon (UMR CNRS 5672))

Co-authors: Peter C. W. Holdsworth (Laboratoire de Physique, ENS de Lyon (UMR CNRS 5672)), Hugo Jacquin (Laboratoire de Physique, ENS de Lyon (UMR CNRS 5672))

### Abstract

Close to a critical point of a continuous phase transition, fluctuations give rise to a so called critical Casimir force $f_{c}$ if the fluctuating medium is confined. This force takes the universal scaling form $f_{c}=L^{-d}\theta(t(L / \xi_{0}^{+})^{1/\nu})$ (L being the size of the system in the confinement direction, t the reduced temperature, $\xi_{0}^{+}$ the non-universal amplitude of the correlation length). Universality allows us to study fluids at liquid/gas continuous phase transition and binary mixtures at mixing/demixing continuous phase transition using Monte-Carlo simulations of the Ising model. Following [2] we calculated $f_{c}$ for a 3 dimensional Ising model in film geometry. Defining a cross-over Hamiltonian which continuously interpolates between a L layer thick system to a L+1 layer thick one, it is possible to compute the derivative of the free-energy with respect to system size L which contains $f_{c}$. The results provided using this method proved to be consistent with experimental results on binary mixture wetting films. We aim at adapting these techniques to study the case of systems in extreme confinement L->0.

References

[1] Andrea Gambassi. The casimir effect : From quantum to critical fluctuations. Journal of Physics : Conference Series, 161 :012037, April 2009. [2] O. Vasilyev, A. Gambassi, A. Macio&#322;ek, and S. Dietrich. Universal scaling functions of critical casimir forces obtained by monte carlo simulations. Physical Review E, 79(4) :041142, April 2009.