On the tricritical Lifshitz behaviour

Marco Zannetti, T. Schneider

The mapping of critical dynamics onto a static (D+1)-dimensional system is analysed in the large-n limit. At criticality Lifshitz tricritical behaviour (with upper critical dimensionality D*=4) occurs in the neighbourhood of an ordinary Lifshitz point (with D*=6). The violation of universality is a consequence of the very special path along which the critical point is approached.

A. L. Lewis

Amnon Aharony A, Eytan Domany, Richard M. Hornreich +2 more

The d-dimensional time-dependent Ginzburg-Landau (TDGL) model is mapped onto a special (d+1)-dimensional model which exhibits a Lifshitz tricritical point (LTP). Many of the LTP critical properties follow from those of the TDGL model, and are shown to belong to a novel universality class of LTP's which results from a (previously ignored) relevant, nonlocal, quartic spin operator. These properties are analyzed with the use of scaling, an \ensuremath{\epsilon} expansion, and the n\ensuremath{\rightarrow}\ensuremath{\infty} limit.

Amnon Aharony A

A.Z. Patashinsky, B.I. Shumilo

Amnon Aharony A, Eytan Domany, Richard M. Hornreich

A renormalization-group analysis of critical behavior near a Lifshitz tricritical point (LTP) is presented, with emphasis on the role played by new, momentum-dependent quartic terms. These result in new stable fixed points which determine the critical behavior. For some values of n (the number of order-parameter components) and m (the dimensionality of the ``soft'' subspace, characterized by quartic momentum-dependent inverse correlation functions), the renormalization-group recursion relations have two stable and accessible fixed points. However, one of these can never be reached in practice, due to a thermodynamic instability which results in a first-order phase transition. For m=d-1, one of the fixed points describes the critical dynamics of the usual n-vector spin model in (d-1) dimensions. This dynamic fixed point also characterizes LTP behavior for large n and n=1. In all other cases, the LTP has new exponents, which are not related to the dynamic model. Our results may be relevant to Lifshitz tricritical behavior in ${\mathrm{RbCaF}}_{3}$ and in some liquid-crystal systems.