Related papers: Comment on "General Method to Determine Replica Sy…
Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the…
Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study $\mathbb Z_2$-symmetry…
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…
We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian…
In these lectures I will review the approach to glasses based on the replica formalism. Many of the physical ideas are very similar to those of older approaches. The replica approach has the advantage of describing in an unified setting…
The spontaneous supersymmetry-breaking that takes place in certain spin-glass models signals a particular fragility in the structure of metastable states of such systems. This fragility is due to the presence of at least one marginal mode…
We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under…
Radiative symmetry breaking (RSB) is a theoretically appealing framework for the generation of mass scales through quantum effects. It can be successfully implemented in models with extended scalar and gauge sectors. We provide a systematic…
The random energy model (REM) is the simplest spin glass model which exhibits replica symmetry breaking. It is well known since the 80's that its overlaps are non-selfaveraging and that their statistics satisfy the predictions of the…
The occurrence of glass transition is believed to be associated to cooperative motion with a growing length scale with decreasing temperature. We provide a novel route to calculate the size of cooperatively rearranging regions CRR of…
Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field…
We consider the quadrupolar glass model with infinite-range random interaction. Introducing a simple one-step replica symmetry breaking ansatz we investigate the para-glass continuous (discontinuous) transition which occurs below (above) a…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous…
Use of dedicated computers in spin glass simulations allows one to equilibrate very large samples (of size as large as $L=32$) and to carry out "computer experiments" that can be compared to (and analyzed in combination with) laboratory…
We construct a real space renormalization group (RG) approach for Ising spin glasses on hypercubic lattices within the scheme of the Migdal-Kadanoff approximation using replicas. Our replica symmetric solution yields results consistent with…
In Phys. Rev. Lett. 110, 219701 (2013) [arXiv:1211.0843] Billoire et al. criticize the conclusions of our Letter [Phys. Rev. Lett. 109, 177204 (2012), arxiv:1206.0783]. They argue that considering the Edwards-Anderson and…
In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step…
The behavior of a newly introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its…
In a recent article, Schmelzer and Tropin [Entropy 20 [2] 103 (2018)] presented an unfounded, confusing critique of several aspects of modern glass science. Relying on pre-Socratic Greek philosophy and state-of-the-art scientific…