arXiv2021
Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature $T_c$ for a one-dimensional Ising spin glass model with diluted long-range interactions. In this model, the probability $P_{ij}$ that an edge $\{i,j\}$ has nonvanishing interaction falls as a power-law with chord distance, $P_{ij}\propto1/R_{ij}^{2σ}$, and we study a range of values of $σ$ with $1/2<σ<1$. We consider a correlation function $C_{4}(r,t)$. A dynamic correlation length that shows power-law growth with time $ξ(t)\propto t^{1/z}$ can be identified in the data and, for large time $t$, $C_{4}(r,t)$ decays as a power law $r^{-α_d}$ with distance $r$ when $r\ll ξ(t)$. The calculation can be interpreted in terms of the maturation metastate averaged Gibbs state, or MMAS, and the decay exponent $α_d$ differentiates between a trivial MMAS ($α_d=0$), as expected in the droplet picture of spin glasses, and a nontrivial MMAS ($α_d\ne 0$), as in the replica-symmetry-breaking (RSB) or chaotic pairs pictures. We find nonzero $α_d$ even in the regime $σ>2/3$ which corresponds to short-range systems below six dimensions. For $σ< 2/3$, the decay exponent $α_d$ follows the RSB prediction for the decay exponent $α_s = 3 - 4 σ$ of the static metastate, consistent with a conjectured statics-dynamics relation, while it approaches $α_d=1-σ$ in the regime $2/3<σ<1$; however, it deviates from both lines in the vicinity of $σ=2/3$.