Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range

Multifractality in spin glasses

We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

Complexity as information in spin-glass Gibbs states and metastates: Upper bounds at nonzero temperature and long-range models

In classical finite-range spin systems, especially those with disorder such as spin glasses, a low-temperature Gibbs state may be a mixture of a number of pure or ordered states; the complexity of the Gibbs state has been defined in the past roughly as the logarithm of this number, assuming the question is meaningful in a finite system. As nontrivial pure-state structure is lost in finite size, in a recent paper [Phys. Rev. E 101, 042114 (2020)2470-004510.1103/PhysRevE.101.042114] Höller and the author introduced a definition of the complexity of an infinite-size Gibbs state as the mutual information between the pure state and the spin configuration in a finite region, and applied this also within a metastate construction. (A metastate is a probability distribution on Gibbs states.) They found an upper bound on the complexity for models of Ising spins in which each spin interacts with only a finite number of others, in terms of the surface area of the region, for all T≥0. In the present paper, the complexity of a metastate is defined likewise in terms of the mutual information between the Gibbs state and the spin configuration. Upper bounds are found for each of these complexities for general finite-range (i.e., short- or long-range, in a sense we define) mixed p-spin interactions of discrete or continuous spins (such as m-vector models), but only for T>0. For short-range models, the bound reduces to the surface area. For long-range interactions, the definition of a Gibbs state has to be modified, and for these models we also prove that the states obtained within the metastate constructions are Gibbs states under the modified definition. All results are valid for a large class of disorder distributions.

Ground-state stability and the nature of the spin glass phase

We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility, critical droplet, and related quantities for both finite- and infinite-volume ground states, we study some of their properties and review three models in which these quantities are partially or fully understood. We also review a recent result showing the connection between our approach and that of disorder chaos. We then view four proposed scenarios for the low-temperature spin glass phase-replica symmetry breaking, scaling-droplet, TNT, and chaotic pairs-through the lens of the predictions of each scenario for the lowest-energy large-lengthscale excitations above the ground state. Using a new concept called σ-criticality, which quantifies the sensitivity of ground states to single-bond coupling variations, we show that each of these four pictures can be identified with different critical droplet geometries and energies. We also investigate necessary and sufficient conditions for the existence of multiple incongruent ground states.