Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions

TL;DR

This study uses extensive Monte Carlo simulations to explore the phase transitions and spin-chirality relationships in a one-dimensional Heisenberg spin glass with long-range interactions, revealing three distinct ordering regimes.

Contribution

It provides a detailed phase diagram and critical properties analysis for different interaction ranges, highlighting the spin-chirality decoupling and coupling phenomena.

Findings

Identified three regimes: coupled order, decoupled order, and zero-temperature order.

Constructed a phase diagram in the interaction exponent versus temperature.

Determined critical properties of chiral-glass and spin-glass transitions.

Abstract

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $\sigma$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $\sigma$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $\sigma$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $\sigma$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $\sigma$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.