Critical exponents for the Lifshitz point: $ε$ expansion

Publisher Website

1 May 1978

journal article
research article
Published by American Physical Society (APS) in Physical Review B

Vol. 17 (9) , 3602-3606
https://doi.org/10.1103/physrevb.17.3602

Abstract

The critical exponents for the biaxial Lifshitz point (

m = 2

) are calculated to leading order in

ε = 5 - d

. The new results are

η_{4} = \frac{- 8 (n + 2) ε^{2}}{27 {(n + 8)}^{2}}

,

β_{k} = 0.5 + \frac{16 (n + 2) ε^{2}}{27 {(n + 8)}^{2}}

, and

η_{2} = \frac{4 (n + 2) ε^{2}}{9 {(n + 8)}^{2}}

. Numerically,

η_{2}

and

η_{4}

are small but the corrections to

β_{k}

are appreciable for

ε = 2

.

Keywords

This publication has 7 references indexed in Scilit:

Low-temperature renormalization group for the Lifshitz point
Physical Review B, 1978
Critical behaviour associated with helical order near a Lifshitz point
Journal of Physics A: General Physics, 1977
A possible lifshitz point for TTF-TCNQ
Solid State Communications, 1977
Physical Realization of a Lifshitz Point in Liquid Crystals
Physical Review Letters, 1977
Helimagnetic-ferromagnetic transition
Physica B+C, 1977
Exactly solvable model exhibiting a multicritical point
Physica A: Statistical Mechanics and its Applications, 1977
Critical Behavior at the Onset of $\vec{k}$ -Space Instability on the $λ$ Line
Physical Review Letters, 1975