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arXiv:cond-mat/0606447 · Journal of Physics Condensed Matter

On the surface critical behaviour in Ising strips: density-matrix renormalization-group study

A. Drzewiński, Anna Maciołek, K Szota

Published May 16, 2006• 2 citations
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Abstract

Using the density-matrix renormalization-group method we study the surface critical behaviour of the magnetization in Ising strips in the subcritical region. Our results support the prediction that the surface magnetization in the two phases along the pseudo-coexistence curve also behaves as for the ordinary transition below the wetting temperature for the finite value of the surface field.

DOI
10.1088/0953-8984/18/22/007

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Using the density-matrix renormalization-group method we study the surface critical behaviour of the magnetization in Ising strips in the subcritical region. Our results support the prediction that the surface magnetization in the two phases along the pseudo-coexistence curve also behaves as for the ordinary transition below the wetting temperature for the finite value of the surface field.
Two-dimensional Ising strips subject to identical surface fields h(1)=h(2) > or =0 are studied for temperatures above and below the bulk critical temperature T(c) and a range of bulk fields h by means of the density-matrix renormalization-group method. In the case of nonvanishing surface fields, the near-critical behavior of the solvation force f(solv), total adsorption Gamma, inverse longitudinal correlation length xi(parallel)( -1) and specific heat C(H) is strongly influenced by the (pseudo) capillary condensation that occurs below T(c). We obtain scaling functions of f(solv), Gamma, and xi(parallel)(-1). C(H) exhibits a weakly rounded singularity on crossing the pseudocoexistence line. We contrast these results with those for the case of free boundaries where, for temperatures slightly below T(c), f(solv) and C(H) exhibit a sharp extremum away from h=0. Our results have direct repercussions for the properties of near-critical Ising films in three dimensions and we argue that the long-ranged solvation (Casimir) force in confined fluids should be more attractive in the neighborhood of the capillary critical point than exactly at the bulk critical point.
We obtain an exact solution of the d = 2 infinite Ising strip with surface fields of opposite signs , . Earlier predictions by Parry et al are confirmed of the crucial importance of wetting for a system confined between two parallel walls that exert competitive surface fields. The transition of the magnetization profile m(z) from the partial wetting regime below the critical wetting temperature at a single wall with a surface field , to the soft-mode single phase in the temperature range , where is the critical temperature of the bulk system, is described in detail. A scaling ansatz is verified for the singular part of the surface excess free energy, and for the profile, . The modification of the magnetization profile near one wall, due to wetting, is studied. Near the (-) wall at the profile is found to be a linear function of the scaled distance but its slope is different than for the case of perfect asymmetry system hence these two cases belong to the different universality regime.
The results of high-accuracy density-matrix renormalization-group calculations for infinite Ising strips of finite widths $40\ensuremath{\leqslant}L\ensuremath{\leqslant}400$ with open boundary conditions are presented. It is shown that in the presence of a small external magnetic field the infinite-system critical power laws can be observed for LLL of the order of hundreds of nanometers. The single power law describes the field dependence of the magnetization or the longitudinal correlation length only on the infinite-system critical isotherm independently of the value of LLL. The approximate power law which describes how the magnetization varies with distance from the infinite-system critical point for several directions in the plane (temperature, external field) is also studied.
Two-dimensional Ising films $L\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ in a nonvanishing bulk magnetic field H are studied at the bulk critical temperature Tc{T}_{c}Tc​ for two choices of surface fields (a) H1=HL=0{H}_{1}{=H}_{L}=0H1​=HL​=0 (ordinary transition), and (b) ${H}_{1}{=H}_{L}=\ensuremath{\infty}$ (normal transition) by the density-matrix renormalization-group method. Universal scaling functions for magnetization profiles, the excess magnetization $\ensuremath{\Gamma},$ the longitudinal correlation length ${\ensuremath{\xi}}_{\ensuremath{\Vert}},$ and for the analog of the solvation force fsolv{f}_{\mathrm{solv}}fsolv​ are found and discussed. When H1=0{H}_{1}=0H1​=0 the scaling function for fsolv{f}_{\mathrm{solv}}fsolv​ has two symmetric minima at $y=\mathrm{sgn}(H)L|H{|}^{\ensuremath{\nu}/\ensuremath{\Delta}}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}1$ with an amplitude at the minimum about 3.8 times the value at H=0,H=0,H=0, the Casimir amplitude. For the normal transition the scaling function for fsolv{f}_{\mathrm{solv}}fsolv​ has a single minimum near the continuation of the pseudocoexistence (capillary condensation) line, with an amplitude about 100 times the Casimir amplitude.