Crossover between ordinary and normal transitions in two dimensional critical Ising films

Abstract

We investigate two dimensional critical Ising films of width L with surface fields H(1)=H(L) in the crossover between ordinary (H(1)=0) and normal (H(1)=infinity) transitions. Using exact transfer-matrix diagonalization and density matrix renormalization-group (DMRG) methods, we calculate magnetization profiles m(z), the excess magnetization Gamma, and the analog of the solvation force f(solv) as functions of H1 for several L. Scaling functions of the above quantities deviate substantially from their asymptotic forms at fixed points for a broad region of the scaling variable LH21 approximately L/l(1), where l(1) is the length induced by the surface field H1. The scaling function for /f(solv)/ has a deep minimum near LH(2)(1)=1, which is about one order of magnitude smaller than its value at both fixed points (the "Casimir" amplitude). For weak H1 (l(1)>L) the magnetization profile has a maximum at the center of the film, and f(solv) decays much faster than L-2. For stronger H1 (1<l(1)<L), the magnetization has two maxima at a distance approximately l(1) from the walls, and the solvation force decays much slower than L-2. For L>>l(1) the solvation force decays according to the universal power law f(solv) approximately L(-2). The results of the approximate DMRG method show remarkable agreement with the exact ones.

Critical phenomena at perfect and non-perfect surfaces

“…that without external fields one would be at the ordinary transition, it has been shown [146,147,148] that a small surface field leads to a short-distance increase of m(z). This critical adsorption in systems with weak surface fields has been studied subsequently in a series of papers [149,150,151,152,153]. The increase of the layer magnetisation is due to the fact that a weak surface field gives rise to a macroscopic length scale, yielding a power law behaviour…”

Effects of weak surface fields on the density profiles and adsorption of a confined fluid near bulk criticality

“…Sufficiently close to bulk criticality one can investigate the regime where D is comparable to l 1 with D, l 1 Ӷ b . In a recent study 13 of the critical dϭ2 Ising film order parameter profiles with two symmetric maxima at zϳl 1 and zϳDϪl 1 were obtained for weak fields h 1 . For even weaker fields when l 1 ϳD the maxima merge into a single one at midpoint, D/2.…”

Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

“…(4.4), as was proposed in [32,35] and employed in the case of the semi-infinite systems in [20,11,21]. Our present investigations of the scaling critical behavior are in complete analogy with the scheme mentioned above [35,11] (see Appendix 2).…”

“…But, the understanding of the situation in the crossover regions between different transitions is less complete. Investigations of the crossover behavior between different surface universality classes for pure isotropic systems have been published in a series of papers [18,10,19,20,11,21]. However, at the present time is open the question about the picture in the crossover regions between the different transitions for the semi-infinite systems with random quenched bulk disorder.…”