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

Citation
A. Maciolek et al., Crossover between ordinary and normal transitions in two dimensional critical Ising films, PHYS REV E, 60(3), 1999, pp. 2887-2896
Citations number
40
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
60
Issue
3
Year of publication
1999
Pages
2887 - 2896
Database
ISI
SICI code
1063-651X(199909)60:3<2887:CBOANT>2.0.ZU;2-#
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=i nfinity) transitions. Using exact transfer-matrix diagonalization and densi ty matrix renormalization-group (DMRG) methods, we calculate magnetization profiles m(z), the excess magnetization Gamma, and the analog of the solvat ion force f(solv) as functions of H-1 for several L. Scaling functions of t he above quantities deviate substantially from their asymptotic forms at fi xed points for a broad region of the scaling variable LH12 similar to L/l(1 ), where l(1) is the length induced by the surface field H-1. The scaling f unction for \f(solv)\ has a deep minimum near LH12 = 1, which is about one order of magnitude smaller than its value at both fixed points (the "Casimi r" amplitude). For weak H-1 (l(1)>L) the magnetization profile has a maximu m at the center of the film, and f(solv) decays much faster than L-2. For s tronger H-1 (l < l(1) < L), the magnetization has two maxima at a distance similar to l(1) from the walls, and the solvation force decays much slower than L-2. For L much greater than l(1) the solvation force decays according to the universal power law f(solv) similar to L-2. The results of the appr oximate DMRG method show remarkable agreement with the exact ones. [S1053-6 51X(99)00209-3].