Critical point shift in a fluid confined between opposing walls

Abstract

The properties of a fluid, or Ising magnet, confined in an $L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ geometry with opposing surface fields at the walls, is 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 $\stackrel{\ensuremath{\rightarrow}}{L}\ensuremath{\infty}$, 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 ${1/L}^{{1+y}_{H}\ensuremath{-}{\ensuremath{\Delta}}_{1}{y}_{T}}$ $({\ensuremath{\Delta}}_{1}$ is the surface gap exponent), with a crossover, for sufficiently large $L$, to a scaling of type ${1/L}^{{1+y}_{H}}$.