Tricritical Lifshitz point in uniaxial ferroelectrics

The critical behavior at a Lifshitz tricritical point in systems with a short-range and uniaxial dipolar interaction is calculated using renormalized group theory. We consider the case in which we separated the wave-vector space into the components k=(${\mathit{p}}_{\mathit{x}}$,${\mathit{p}}_{\mathit{y}}$,q), with the dimensions m̃, m, and d-m-m̃ for ${\mathit{p}}_{\mathit{x}}$, ${\mathit{p}}_{\mathit{y}}$, and q, respectively. The upper critical dimension ${\mathit{d}}_{\mathit{c}}$ was found to be ${\mathit{d}}_{\mathit{c}}$=2+[(2m+m̃)/3]. The critical exponents and the logarithmic corrections have been calculated and compared with the available experimental and theoretical data. © 1996 The American Physical Society.