2003
DOI: 10.1103/physrevb.68.224428
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Boundary critical behavior atm-axial Lifshitz points for a boundary plane parallel to the modulation axes

Abstract: The critical behavior of semi-infinite d-dimensional systems with n-component order parameter φ and short-range interactions is investigated at an m-axial bulk Lifshitz point whose wave-vector instability is isotropic in an m-dimensional subspace of R d . The associated m modulation axes are presumed to be parallel to the surface, where 0 ≤ m ≤ d − 1. An appropriate semi-infinite |φ| 4 model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usu… Show more

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Cited by 10 publications
(60 citation statements)
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“…However, when considering FBC, we shall restrict ourselves in two ways: We assume that the BC that result in the large length-scale limit (i) do not break the O(n) symmetry and (ii) are associated with the respective most stable renormalization-group (RG) fixed point. For parallel orientation this simply means that Dirichlet BC φ = 0 hold asymptotically [22,23,24,25]. In the case of perpendicular orientation, two BC hold on either ‡ Note that since ξα and ξ β are bulk correlation lengths, they diverge at the bulk critical point.…”
Section: Introductionmentioning
confidence: 99%
“…However, when considering FBC, we shall restrict ourselves in two ways: We assume that the BC that result in the large length-scale limit (i) do not break the O(n) symmetry and (ii) are associated with the respective most stable renormalization-group (RG) fixed point. For parallel orientation this simply means that Dirichlet BC φ = 0 hold asymptotically [22,23,24,25]. In the case of perpendicular orientation, two BC hold on either ‡ Note that since ξα and ξ β are bulk correlation lengths, they diverge at the bulk critical point.…”
Section: Introductionmentioning
confidence: 99%
“…The discovery of the existence of this kind of multicritical points in 1975 led to numerous theoretical studies of their bulk critical properties. With the exception of an early attempt by Gumbs [114], surface critical phenomena at a bulk Lifshitz point have only been studied very recently [115,116,117,118,119,120]. Most of the results have been obtained for the semi-infinite ANNNI model.…”
Section: Surface Critical Behaviour Near a Lifshitz Pointmentioning
confidence: 98%
“…Very recently Diehl and coworkers [119,120] analysed the surface critical behaviour at bulk Lifshitz points using renormalization group methods. They thereby considered general m-axial Lifshitz points where the wave vector instability takes place in an mdimensional subspace of the d-dimensional space.…”
Section: Surface Critical Behaviour Near a Lifshitz Pointmentioning
confidence: 99%
“…The function A (u,wϭ0) has been computed to one-loop order in Ref. 27. Its explicit form will not be needed in the following.…”
Section: A General Anisotropy: Renormalization and Rg Equationsmentioning
confidence: 99%
“…27, we have included a renormalization function A (u,w) to absorb momentum-independent poles proportional 2 of the two-point vertex function. The fact that the theory must reduce for wϭ0 to the m-isotropic one implies the relations…”
Section: A General Anisotropy: Renormalization and Rg Equationsmentioning
confidence: 99%