Bulk and boundary critical behavior at Lifshitz points

Pramana

H W Diehl1¹ 

[1] Fachbereich Physik, Universität Duisburg-Essen, Campus Essen, D-45117 Essen, Germany$$

关键词: Critical behavior;    Lifshitz points;    field theory;    boundary critical behavior;    anisotropic scale invariance.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Lifshitz points are multicritical points at which a disordered phase, a homogeneous ordered phase, and a modulated ordered phase meet. Their bulk universality classes are described by natural generalizations of the standard 𝜙4 model. Analyzing these models systematically via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the middle of 1970s. We survey the recent progress made in this direction, discussing results obtained via dimensionality expansions, how they compare with Monte Carlo results, and open problems. These advances opened the way towards systematic studies of boundary critical behavior at 𝑚-axial Lifshitz points. The possible boundary critical behavior depends on whether the surface plane is perpendicular to one of the 𝑚 modulation axes or parallel to all of them. We show that the semi-infinite field theories representing the corresponding surface universality classes in these two cases of perpendicular and parallel surface orientation differ crucially in their Hamiltonian's boundary terms and the implied boundary conditions, and explain recent results along with our current understanding of this matter.

【 授权许可】

Unknown