# Precursors of the Spin Glass Transition in Three Dimensions

## TL;DR

This paper investigates the energy landscape and dynamics of the 3D Heisenberg Spin Glass model in the paramagnetic phase, identifying precursor phenomena to the spin glass transition and drawing parallels with supercooled liquids.

## Contribution

It uncovers non-trivial landscape features and dynamical crossovers above the critical temperature, providing insights into the phenomenology of spin glasses in three dimensions.

## Key findings

- Onset of non-trivial landscape behavior at temperature T_o
- Power-law growth of relaxation times indicating a dynamical crossover at T_d
- Efficient energy minimization using Successive Overrelaxation algorithm

## Abstract

We study energy landscape and dynamics of the three-dimensional Heisenberg Spin Glass model in the paramagnetic phase, i.e. for temperature $T$ larger than the critical temperature $T_\mathrm{c}$. The landscape is non-trivially related to the equilibrium states even in the high-temperature phase, and reveals an onset of non-trivial behavior at a temperature $T_\mathrm{o}$, which is also seen through the behavior of the thermoremanent magnetization. We also find a power-law growth of the relaxation times far from the spin-glass transition, indicating a dynamical crossover at a temperature $T_\mathrm{d}$, $T_\mathrm{c}<T_\mathrm{d}<T_\mathrm{o}$. The arising picture is reminiscent of the phenomenology of supercooled liquids, and poses questions on which mean-field models can describe qualitatively well the phenomenology in three dimensions. On the technical side, local energy minima are found with the Successive Overrelaxation algorithm, which reveals very efficient for energy minimization in this kind of models.