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arXiv:cond-mat/9610161 · Nuclear Physics B

Critical adsorption in systems with weak surface field: The renormalization-group approach

Alina Ciach, Uwe Ritschel

Published Apr 1, 1997• 25 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(97)00015-1

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We study the surface critical behavior of semi-infinite systems with an n-component order parameter and short-range interactions at a bulk tricritical point. The special surface transition is investigated in detail for space dimensionalities d=3-\ensuremath{\epsilon}\ensuremath{\le}3 using field-theoretic renormalization-group methods. For \ensuremath{\epsilon}>0 its infrared-stable fixed point is described by a Hamiltonian which contains a \ensuremath{\Vert}\ensuremath{\varphi}\ensuremath{\rightarrow}${\ensuremath{\Vert}}^{4}$ surface interaction of strength O(${\ensuremath{\epsilon}}^{1/2}$) in addition to the familiar \ensuremath{\Vert}\ensuremath{\varphi}\ensuremath{\rightarrow}${\ensuremath{\Vert}}^{6}$ bulk interaction of strength O(\ensuremath{\epsilon}). For d\ensuremath{\equiv}3, logarithmic corrections of a non-power-law form appear. The renormalization of a proper continuum model is expounded and the implications of the results are discussed, especially with regard to the adsorption of polymers from a \ensuremath{\theta} solution.
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.