Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass

TL;DR

This study uses extensive Monte Carlo simulations to demonstrate that in a three-dimensional Heisenberg spin glass, chiral and spin orderings occur at distinct nonzero temperatures, with the chiral-glass transition belonging to a different universality class.

Contribution

It provides numerical evidence for separate chiral and spin glass transitions and estimates critical exponents, highlighting the decoupling and distinct universality class of the chiral-glass transition.

Findings

Chiral and spin glass transitions occur at different nonzero temperatures.

Chiral-glass exponents are estimated as rac{1.4 b1 0.2}{b1 0.2} and rac{0.6 b1 0.2}{b1 0.2}.

Chiral-glass state is non-self-averaging and may involve replica-symmetry breaking.

Abstract

The nature of the ordering of the three-dimensional isotropic Heisenberg spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. Several independent physical quantities are measured both for the spin and for the chirality, including the correlation-length ratio, the Binder ratio, the glass order parameter, the overlap distribution function and the non-self-averageness parameter. By controlling the effect of the correction-to-scaling, we have obtained a numerical evidence for the occurrence of successive chiral-glass and spin-glass transitions at nonzero temperatures, T_{CG} > T_{SG} > 0. Hence, the spin and the chirality are decoupled in the ordering of the model. The chiral-glass exponents are estimated to be \nu_{CG}=1.4+-0.2 and \eta_{CG}=0.6+-0.2, indicating that the chiral-glass transition lies in a universality class different from that of the Ising spin glass. The possibility that the spin and chiral sectors undergo a simultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass state turns out to be non-self-averaging, possibly accompanying a one-step-like peculiar replica-symmetry breaking. Implications to the chirality scenario of experimental spin-glass transitions are discussed.