Critical point shift in a fluid confined between opposing walls

Details Critical point shift in a fluid confined between opposing walls Critical point shift in a fluid confined between opposing walls

1997-09-16

arxiv.org/abs/cond-mat/9709176v2

Phys. Rev. E 57, 2626 (1998)

Physics

Condensed Matter

Statistical Mechanics

9 pages, RevTeX, 11 PostScript figures included. Minor corrections. Final version as published

Scientific paper

10.1103/PhysRevE.57.2626

The properties of a fluid, or Ising magnet, confined in a $L \times \infty$ geometry with opposing surface fields at the walls are studied by density matrix renormalization techniques. In particular we focus on the effect of gravity on the system, which is modeled by a bulk field whose strength varies linearly with the distance from the walls. It is well known that in the absence of gravity phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores phase coexistence up to the bulk critical temperature, in agreement with previous mean field results. A detailed study of the scaling to the critical point, as $L \to \infty$, is performed. The temperature shift scales as $1/L^{y_T}$, while the gravitational constant scales as $1/L^{1+y_H}$, with $y_T$ and $y_H$ the bulk thermal and magnetic exponents respectively. For weak surface fields and $L$ not too large, we also observe a regime where the gravitational constant scales as $1/L^{1+y_H - \Delta_1 y_T}$ ($\Delta_1$ is the surface gap exponent) with a crossover, for sufficiently large $L$, to a scaling of type $1/L^{1+y_H}$.

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