Related papers: Replica Symmetry Breaking in Short-Range Spin Glas…
We prove the impossibility of recent attempts to decouple the Replica Symmetry Breaking (RSB) picture for finite-dimensional spin glasses from the existence of many thermodynamic (i.e., infinite-volume) pure states while preserving another…
In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method…
We perform the replica symmetry breaking (RSB) in the vicinity of the point of instability of the replica symmetric solution in the model of axial quadrupolar glass. It is shown that the solution with the first stage RSB is stable against…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…
By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full…
Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory,…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
In this topical review we discuss the nature of the low-temperature phase in both infinite-ranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or ``observable'',…
During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick…
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…
Here we review the approach to glassy systems based on the replica method and we introduce the main ingredients of replica symmetry breaking. We explain why the replica method has been successful in spin glass and why it should be…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
A short survey is presented on spin--glass--like states characteristics in complex nonmagnetic systems. We discuss the interplay of the interaction structure and symmetry with the classification scenarios of the replica symmetry breaking.…
We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent…
There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on $[0,1]$, where the measure represents the similarity (or "overlap") of two independently sampled…