Crossover aspects in Ising strips under the influence of variable surface fields and a grain boundary

Abstract

I use an exact variational formulation of Mikheev and Fisher to study the critical Ising strip with a grain boundary and confining surfaces characterized by arbitrary and different surface magnetic fields. Energy density profiles that serve as order parameters of the system within the used method show strong nonmonotonous behavior in the vicinity of confining surfaces. I consider short-distance expansion of energy density profiles. New universal amplitudes associated with distant-wall corrections exhibit nontrivial crossover behaviors from positive to negative values as the field's variables are continuously varied. Casimir amplitudes calculated in a self-contained manner are characterized by complex manifolds which may comprise two disconnected positive wings separated by an area of negative values. I define and determine the generalized de Gennes-Fisher amplitude, which strongly suggests that a stress tensor is present within one of the distant-wall corrections. This is an unanticipated result given that a similar discovery for standard extraordinary (E) and ordinary (O) surface universality classes was based on the conformal invariance symmetry, which is broken under the present boundary conditions. A grain boundary essentially influences both energy density profiles and Casimir amplitudes, besides surface fields with a number of accompanying features that are examined in detail. We present closed analytic forms of energy density profiles for standard (N) and (O) BCs: ɛNN(x,g),ɛOO(x,g),ɛNO(x,g) [(N) is the normal surface universality class, g is the grain boundary's strength, x is the relative distance x:=z/L with L as a film width], thus enabling us to deduce their important symmetry properties and to have a detailed insight into their general behaviors.

Critical Casimir Effect: Exact Results

“…• exact variational approach due to Mikheev and Fisher applied to the Ising model [160,180,182,192,199,202] • studies using numerical density-matrix renormalization-group techniques [147,147,149,150,152,159,163] • studies based on renormalization-group theory using the ε-expansion technique [115,116,258,[280][281][282][283][284][285][286] • studies using fixed dimension d techniques [258,259,[286][287][288] of O(n)-symmetric models…”

Manipulation and amplification of the Casimir force through surface fields using helicity

“…For example, in [7] the critical thermal noise in a solvent medium consisting of a binary liquid mixture of water and 2,6-lutidine near its lower consolute point is shown to lead to attractive or repulsive forces, depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture. On the theoretical side, the influence of the surface fields has been studied on the case of two dimensional Ising model via exact calculation [11][12][13][14], using the variational formulation due to Mikheev and Fisher [15,16], with the help of density-matrix renormalization-group numerical method [17][18][19][20], via conformal invariance [21,22], Monte Carlo methods [21], and numerically using bond propagation algorithms [23]. The three dimensional Ising model has been studied with Monte Carlo methods in [24][25][26][27][28][29][30], mean-field type calculations [31][32][33][34][35][36] and renormalized local functional theory [37].…”