Renormalization-group analysis of chiral transitions

Abstract

Chiral phase transitions are analyzed by renormalization-group techniques on the basis of a standard Ginzburg-Landau-Wilson Hamiltonian for two real n-component fields a and b with quartic couplings u${(\mathrm{a}}^{2}$${+\mathrm{b}}^{2}$${)}^{2}$ and v[(a\ensuremath{\cdot}${\mathrm{b})}^{2}$${\mathrm{\ensuremath{-}}\mathrm{a}}^{2}$${\mathrm{b}}^{2}$]. This model is a natural extension of the usual ${\mathrm{cphi}}^{4}$ O(n) model: For v>0, it represents triangular antiferromagnets, helical magnets, and the A phase of superfluid $^{3}\mathrm{He}$. An \ensuremath{\epsilon}=4-d expansion reveals a new v>0, chiral fixed point which is stable for n>21.8-23.4\ensuremath{\epsilon}+O(${\ensuremath{\epsilon}}^{2}$). An antisymmetric chirality tensor, \ensuremath{\kappa}=${a}_{\ensuremath{\lambda}}$${b}_{\ensuremath{\mu}}$-${a}_{\ensuremath{\mu}}$${b}_{\ensuremath{\lambda}}$, is a new relevant operator at this fixed point. The associated exponents \ensuremath{\gamma} and \ensuremath{\nu} are smaller than the usual O(n) exponents. A 1/n expansion yields a continuous chiral transition for 2<d<4, the exponents \ensuremath{\gamma} and \ensuremath{\nu} again being smaller than in the O(n) case. The chiral crossover exponent, ${\ensuremath{\varphi}}_{\ensuremath{\kappa}}$, exceeds \ensuremath{\gamma} in both \ensuremath{\epsilon} and 1/n expansions. The spectrum of other leading scaling operators and their exponents is obtained. On the basis of comparisons with recent Monte Carlo and experimental results, it is argued that the chiral fixed point probably remains stable down to the physically relevant cases n=2 and 3 at d=3.