Nature of the phase transition of the three-dimensional isotropic Heisenberg spin glass

TL;DR

This study uses extensive Monte Carlo simulations to investigate the phase transition in the three-dimensional isotropic Heisenberg spin glass, revealing a chiral-glass long-range order at finite temperatures without conventional spin-glass order.

Contribution

It provides new insights into the nature of phase transitions in the 3D Heisenberg spin glass, emphasizing the role of chiral-glass order and addressing discrepancies with previous studies.

Findings

Chiral-glass order exists at finite temperatures without spin-glass order.

Identification of crossover scales between spin-chirality coupling and decoupling regimes.

Discussion on the cause of discrepancies with recent numerical works.

Abstract

Equilibrium properties of the three-dimensional isotropic Heisenberg spin glass are studied by extensive Monte Carlo simulations, with particular attention to the nature of its phase transition. A finite-size-scaling analysis is performed both for the spin-glass (SG) and the chiral-glass (CG) orders. Our results suggest that the model exhibits the CG long-range order at finite temperatures without accompanying the conventional SG long-range order, in contrast to some of the recent works claiming the simultaneous SG and CG transition. Typical length and time scales which represent a crossover from the spin-chirality coupling regime at short scales to the spin-chirality decoupling regime at long scales are introduced and examined in order to observe the true asymptotic transition behavior. On the basis of these crossover scales, discussion is given concerning the cause of the discrepancy between our present result and those of other recent numerical works.