Related papers: Generic proving of replica symmetry breaking
A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly…
Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful \emph{fully lifted} (fl) statistical interpolating/comparison mechanism for bilinearly indexed random processes. Here, we present a particular realization of such fl…
Spin glass theory, as a paradigm for describing disordered magnetic systems, constitutes a prominent subject of study within statistical physics. Replica symmetry breaking (RSB), as one of the pivotal concepts for the understanding of spin…
[104] introduced a powerful \emph{fully lifted} (fl) statistical interpolating mechanism. It established a nested connection between blirps (bilinearly indexed random processes) and their decoupled (linearly indexed) comparative…
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the…
We consider \emph{bilinearly indexed random processes} (blirp) and study their interpolating comparative mechanisms. Generic introduction of the \emph{fully lifted} (fl) blirp interpolation in [105] was followed by a corresponding…
In our companion paper \cite{Stojnicgscomp16} we introduce a collection of fairly powerful statistical comparison results. They relate to a general comparison concept and its an upgrade that we call lifting procedure. Here we provide a…
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…
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…
The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation between the expectation value of the…
We analyze the full replica symmetry breaking (full--RSB) free energy functional for the Ising spin glass on a random regular graph proposed by the author in \cite{MyPaper}. We prove that the full--RSB formulation provides an improvement…
For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered…
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…
We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by…
The recent reports of the replica symmetry breaking (RSB) phenomenon in photonic experiments [1-5] boosted the understanding of the role of disorder in multimode lasers, as well as helped to settle enlightening connections [6-13] with the…
We describe a novel method which allows the treatment of high orders of replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly, without a need for approximations or scaling assumptions. It yields the low temperature…
In this short note, we present supporting evidence for the replica symmetric approach to the random bond q-state Potts models. The evidence is statistically strong enough to reject the applicability of the Parisi replica symmetry breaking…
We study the replica field theory which describes the pinning of elastic manifolds of arbitrary internal dimension d in a random potential, with the aim of bridging the gap between mean field and renormalization theory. The full effective…
We derive, within the replica formalism, a generalisation of the Crisanti-Sommers formula to describe the large deviation function (LDF) ${\cal L}(e)$ for the speed-$N$ atypical fluctuations of the intensive ground-state energy $e$ of a…
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,…