Surface critical behaviour of fluids and magnets

Abstract

The surface critical behaviour of fluids was studied by extensive computer simulations of the liquid–vapour coexistence curves of water and the LJ fluid in pores. The local order parameter , that is the difference between the densities of the coexisting phases at distance z from the surface, follows the surface critical behaviour of the ordinary transition of Ising magnets, Δρ∼τ^β₁ , where τ = 1 − T/T _c is the temperature deviation from the bulk critical temperature T _c and β₁ ≈ 0.8. The crossover from bulk to surface critical behaviour occurs when the distance to the wall is about two bulk correlation lengths ξ₋. The temperature dependence of the local coexistence curve diameter shows mainly regular behaviour. To provide equivalence of the surface critical behaviour of fluids and Ising magnets, we propose to generalize the definition of the order parameter of the phase transition of Ising magnets in the presence of a surface field. The difference of the local magnetizations in the coexisting phases, and not the local magnetization m ^I,II(z) itself, measures the dissimilarity of the coexisting phases and should be considered as the correct order parameter. The order parameter contributes to the total magnetization up to T _c only. Accordingly, the average magnetization is induced by the surface field and does not vanish above T _c.

Keywords:

• Surface critical behaviour
• Fluids
• Magnets

Acknowledgements

We are grateful to K. Binder, M. Fisher, R. Evans, H.W. Diehl and J. Indekeu for stimulating and helpful discussions. Financial support from DFG (SPP 1155) and BMBF (grant 01SF0303) is gratefully acknowledged.