The Theory of Boundary Critical Phenomena

Diehl, H. W.

doi:10.1142/s0217979297001751

Cited by 321 publications

(513 citation statements)

References 52 publications

Supporting

Mentioning

493

Contrasting

Order By: Relevance

“…It turns out that within MFT, this issue can be fully resolved in terms of a modified DA for fictitious (+, o) BCs if the location and the curvature of the actual interface at x = 0 are known. Note, however, that this mapping onto a fictitious ersatz colloid with Dirichlet BC is not expected to hold beyond MFT, because the intrinsic order parameter profile vanishes at z 0 (x) linearly ∝ z − z 0 (x), whereas at a Dirichlet wall it vanishes ∝ (z − z 0 (x)) (β 1 −β )/ν , where β 1 is a surface critical exponent (β 1 (d = 4) = 1, β 1 (d = 3) ≃ 0.8 [11]). Thus, within MFT (β 1 − β )/ν happens to be equal to 1, too, whereas in d = 3 (β 1 − β )/ν ≃ 0.8.…”

Section: B Mft Scaling Functions For An Infinitely Extended Cylindermentioning

confidence: 99%

See 1 more Smart Citation

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

et al. 2014

View full text Add to dashboard Cite

Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.

show abstract

Section: B Mft Scaling Functions For An Infinitely Extended Cylindermentioning

confidence: 99%

“…These fluctuation-induced interactions can be described in terms of universal scaling functions determined by the bulk and surface universality classes of the system [9][10][11]. Simple fluids and binary liquid mixtures belong to the Ising universality class.…”

Section: Introductionmentioning

confidence: 99%

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Among the main reasons for that rapid and successful development we can mention the interest in understanding the physics of low-dimensional systems and an immense potential of industrial applications of thin films [1][2][3]. In particular, theoretically it has been shown that systems of continuous spins (XY and Heisenberg) in two dimensions (2D) with short-range interaction cannot have long-range order at finite temperature [4].…”

Section: Introductionmentioning

confidence: 99%

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Hoang¹,

Kasperski²,

Puszkarski³

et al. 2013

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper which correspond to the 3-state Potts model. The Hamiltonian of the system includes: (i) the exchange interaction Jij between nearest-neighbor sites i and j (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance rc (iii) a single-ion perpendicular anisotropy of amplitude A. We allow Jij = Js between surface spins, and Jij = J otherwise. We show that the ground state depends on the the ratio D/A and rc. For a single layer, for a given A, there is a critical value Dc below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near Dc: the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T , below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio Js/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.

show abstract

“…First developed for static equilibrium bulk critical behavior, this classification scheme has subsequently been extended both to dynamic bulk critical behavior [2] as well as to static surface critical behavior of semi-infinite systems at bulk critical points [3,4].…”

mentioning

confidence: 99%

“…Owing to the O(3) symmetry, the surface of such a d=3-dimensional system cannot spontaneously order for J 1 /J < ∞. Hence the surface transition that occurs at the bulk critical point T = T c is the so-called ordinary one [4]. Its critical indices can be expressed in terms of two independent bulk exponents, e.g., η and ν, and one surface exponent, e.g., the correlation exponent η ord .…”

mentioning

confidence: 99%

Dynamic surface critical behavior of isotropic Heisenberg ferromagnets

Krech¹,

Karl²,

Diehl³

2001

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

The effects of free surfaces on the dynamic critical behavior of isotropic Heisenberg ferromagnets are studied via phenomenological scaling theory, field-theoretic renormalization group tools, and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed, the boundary terms of the associated dynamic field theory are identified, its renormalization in d ≤ 6 dimensions is clarified, and the boundary conditions it satisfies are given. Scaling laws are derived which relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar static bulk and surface exponents. Accurate computer-simulation data are presented for the dynamic surface structure factor; these are in conformity with the predicted scaling behavior and could be checked by appropriate scattering experiments.

show abstract

The Theory of Boundary Critical Phenomena

Cited by 321 publications

References 52 publications

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

Dynamic surface critical behavior of isotropic Heisenberg ferromagnets

Contact Info

Product

Resources

About