Ordering and broken symmetry in short-ranged spin glasses

Abstract

In this topical review we discuss the nature of the low-temperature phase in both infiniteranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or "observable", states and (probably) unphysical, "invisible" states. We review replica symmetry breaking, and describe what it would mean in shortranged spin glasses. We introduce the notion of thermodynamic chaos, which leads to the metastate construct. We apply these tools to short-ranged spin glasses, and conclude that replica symmetry breaking, in any form, cannot describe the low-temperature spin glass phase in any finite dimension. We then discuss the remaining possible scenarios that could describe the low-temperature phase, and the differences they exhibit in some of their physical properties -in particular, the interfaces that separate them. We also present rigorous results on metastable states and discuss their connection to thermodynamic states. Finally, we discuss some of the differences between the statistical mechanics of homogeneous systems and those with quenched disorder and frustration.

Spin Glasses. Still Complex After All These Years?

“…In what follows, I list several features -some recently uncovered, some not -in which spin glasses display unexpected behavior ('unexpected' meaning 'not familiar from our experience with the statistical mechanics of homogeneous systems'). A similar discussion appears in [31], and much of it represents joint work with Chuck Newman.…”

“…The correct order parameter needs to describe the structure and relationships among the infinitely many states present at low temperature. (We ignore here the problems inherent in defining 'pure state' for the SK model; for more discussion on this, see [30,31,32].) To do this, we consider the overlap between two states α and β, at fixed J and T :…”

A Percolation-theoretic Approach to Spin Glass Phase Transitions

“…, ultrametricity is the property that Q (2) = Q (3) . The issue of percolation signatures for ultrametricity in the SK model is treated at length in [22].…”

“…We simulated the three-dimensional ±J Edwards-Anderson model on skew periodic cubic lattices for system sizes 6 3 , 8 3 , 10 3 and 12 3 . For each size we simulated 100 realizations of disorder for 50,000 Monte Carlo sweeps of which the first 1/4 of the sweeps were for equilibration and the remaining 3/4 for data collection.…”

Strongly correlated Fermi–Bose mixtures in disordered optical lattices

“…In particular, this provides bond frustration, which is essential for the appearance of the spin glass phase and turns out to introduce severe difficulties for analytical and numerical analyses. We thus think that experiments with ultracold atoms can provide a useful quantum simulator to address challenging questions related to spin glasses such as the nature of the ordering of its ground-and possibly metastable states [4,39,40], broken symmetry and dynamics of spin glasses [5,41]. In the following two sections, we outline some general properties of spin glasses and then we apply the replica method under the constraint of a fixed magnetization and argue that this preserves the occurrence of a symmetry breaking characteristics of spin glasses in the Mézard-Parisi theory [4].…”