Capillary condensation in a square geometry with surface fields

We study the influence of wetting on capillary condensation for a simple fluid in a square geometry with surface fields, where the reference system is an infinitely long slit. The corner transfer matrix renormalization group method has been extended to study a two-dimensional Ising model confined in an $L\times L$ geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.

Figure 1

The critical wetting lines for semi-infinite systems at $T=2.1$: the corner wetting [$h_{cw}\left(T\right)$] on the two planar surfaces forming a straight angle and wetting [$h_w\left(T\right)$] on the planar surface. With respect to the planar wetting, $h_1=0.1$ and $0.275$ correspond to the dry regime, whereas $h_1=0.371$ and $0.5$ correspond to the wet one.

Figure 2

Pseudocoexistence lines for the square (triangles) and slit (circles) systems for $L=500$ and $h_1=0.8$. $L$ is measured in units of lattice constant, whereas $h_1$ is in $J$ units.

Figure 3

Two-dimensional magnetization profiles $\langle s_{i,j}\rangle$ on the square geometry $31\times 31$ for the two values of the surface field $h_1=0.1$ (left-hand graphs) and $h_1=0.6$ (right-hand graphs) calculated at fixed temperature $T=2.0$. The profiles change their shapes and spin polarizations while varying the bulk field value $H$ below and above the wetting temperature $T_w(h_1=0.1)=2.257$ and $T_w(h_1=0.6)$ $=$ 1.814, respectively.

Figure 4

Plots of the local exponent for both geometries at $T=2.1$. Lines correspond to the square geometry, whereas the symbols are related to the slit one.

Figure 5

The effective exponents $\alpha \left(L\right)$ and their fitting curves denoted by the thick lines for two sample values of the surface field: $h_1=0.1$ for the dry system and $h_1=0.5$ for the wet system [see Fig. (1)].