Abstract
A three-dimensional anisotropic sine-Gordon model, derived as the spin-wave approximation to the biaxial () Lifshitz point problem in a uniform magnetic field, is shown to possess [in close analogy to the isotropic two-dimensional (2D) sine-Gordon theory which is well known to describe the critical behavior of the 2D model], a surface of infinite-order phase transitions. This critical surface separates a phase characterized by infinite correlation length and power-law decay of correlations, and controlled by a stable fixed line, from one with finite and exponential decay. As the critical surface is approached from the latter phase, diverges as exp () where is a universal number, measures the distance from the critical surface, and is nonuniversal. On the critical surface correlations decay like , where and . Speculations on the occurrence of an infinite-order transition in liquid-crystal mixtures exhibiting nematic, smectic-, and smectic- phases are advanced.
- Received 23 September 1980
DOI:https://doi.org/10.1103/PhysRevB.23.4615
©1981 American Physical Society