arXiv subjects

Enzo Marinari

Publications and source records attributed to Enzo Marinari.

At least 19 recordsLinked to original sources

arXiv2026

Ornstein-Uhlenbeck Process Driven by Multiple Dichotomous Noises

We study a generalized Ornstein-Uhlenbeck process driven by a superposition of $K$ independent dichotomous noises with arbitrary fixed amplitudes and switching rates. Unlike the classical Ornstein-Uhlenbeck process driven by equilibrium Gaussian white noise, the present system is governed by bounded nonequilibrium fluctuations with finite correlation times. We obtain exact expressions for the stationary position distribution and all cumulants, and show that the stationary state possesses an unexpectedly rich structure, including compact support, algebraic branch-point singularities, edge divergences, and multiple extrema. We establish a mapping onto a heterogeneous random-flight process with bounded jumps, yielding a transparent probabilistic interpretation of the stationary measure. We further analyze several limiting regimes, including the crossover to Gaussian statistics for large numbers of noise sources. For ensembles with exponentially-distributed quenched amplitudes, we derive exact disorder-averaged stationary distributions and show that disorder fundamentally alters the stationary state, producing exponential tails decorated by algebraic prefactors with non-trivial exponents.

cond-mat.stat-mech↗

arXiv2026

Cluster moves with an entropic reservoir accelerate low-temperature simulations of three-dimensional spin glasses

We present an algorithm for the simulation of three-dimensional spin glasses deep in the low-temperature phase: Parallel Tempering enhanced with Houdayer moves and with an entropic reservoir (PTHR). Although differences with the standard Houdayer algorithm are small, PTHR allows us to equilibrate a large number of samples of $L=16$ lattices with Gaussian couplings for temperatures $T\geq 0.2$. We show that the computational complexity displays better size scaling than standard Parallel Tempering. For finite sizes, our method outperforms other cluster algorithms by a speedup factor of around 64. In close analogy with standard Parallel Tempering, PTHR's computational complexity strongly relates to temperature chaos.

cond-mat.dis-nn↗

arXiv2026

On the true low-energy excitations of the three-dimensional spin glass

We study the low-energy excitations of the three dimensional spin glass through a large-scale Monte Carlo simulation on lattices up to $L=18$. We find smooth extrapolations down to zero temperature, which, in the case of the energy and of the link overlap, can be directly -- and favourably -- compared with previous investigations featuring ground states (i.e., at zero temperature). The best fit for the fractal dimension of the excitations is provided by Replica-Symmetry Breaking theory, but we also consider the alternative TNT description. The $P(q)$ is found to verify the Parisi-Toulouse temperature scaling. Our data provides a spectacular confirmation of the overlap-equivalence hypothesis.

cond-mat.dis-nn↗

arXiv2026

Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model

We investigate the first two moments of the critical internal energy $E$ in a weakly disordered two-dimensional Baxter eight-vertex model as a function of the system size $L$, evaluated at the pseudo-critical point. Disorder is introduced via an equivalent representation of the pure eight-vertex model in terms of two ferromagnetic Ising models coupled by a four-spin interaction of strength $g_0$, where the Ising couplings consist of a uniform ferromagnetic part $J>0$ supplemented by weak Gaussian spatial disorder. In the critical regime, the model is formulated in terms of interacting Grassmann-Majorana spinor fields with quartic interactions and analyzed, for small positive $g_0$, using a combination of replica and renormalization-group methods. We also run extensive numerical simulations measuring the critical internal energy. Our results show that its relative variance increases with $L$ and approaches a finite constant as $L \to \infty$ for both $\pm g_0$. Hence, fluctuations remain relevant independently of the sign of $g_0$ (and thus of the specific-heat exponent), implying a lack of self-averaging of both the critical internal energy and the free energy. Consequently, reliable estimates of these quantities require averaging over many disorder realizations. In addition, we numerically confirm earlier predictions concerning the absence of self-averaging of the critical internal energy in the disordered Ising model.

cond-mat.stat-mech↗

arXiv2026

Nonconvex optimization methods for ground states in disordered continuous-spin models

This work explores the global optimization problem of finding lowest-energy configurations in disordered continuous-spin models from statistical physics, with a particular focus on the random field XY model. Due to an extremely non-convex nature of the associated energy landscape, this problem remains highly challenging. From an optimization perspective, we reformulate the traditional angular Hamiltonian as a constrained problem on the Cartesian product of spheres, allowing the application of Riemannian optimization techniques, which show better computational performance. We design a family of Basin Hopping algorithms whose perturbation mechanisms are specifically designed to exploit the structure of the underlying physical model, and further extend them within a Population Basin Hopping framework. The proposed methods are evaluated against optimization algorithms widely used in computational physics. The proposed variants turn out to be the most effective method in the comparison, consistently attaining lower-energy configurations within the same computational budget. This work establishes a robust link between continuous-spin systems and continuous global optimization, providing a high-performance benchmark for exploring complex energy landscapes.

math.OC↗

arXiv2026

Dreaming improves memorization in a Hopfield model with bounded synaptic strength

The Hopfield model provides a paradigmatic framework for associative memory. Its classical implementation, based on the Hebbian learning rule, suffers from catastrophic forgetting: when one attempts storing too many patterns, the network fails to retrieve any of them. Yet, the Hebbian rule does not take into account that synaptic strength is bounded. Introducing this biologically plausible modification, known as "clipping", eliminates catastrophic forgetting; the model is now able to retrieve the most recently seen memories, eliminating older ones. Yet, its memorization capacity is much reduced with respect to the unclipped case. Here, we investigate the effects of adding a "dreaming" phase on the capacity of a clipped Hopfield model. Following a proposal by Hopfield, Feinstein and Palmer, we assume that during the dreaming phase, the model generates random patterns that are then "unlearned". We show that while clipping still removes catastrophic forgetting, alternating learning and dreaming phases improves the memorization capacity and makes the search for optimal performance more realistic from an evolutionary perspective.

cond-mat.dis-nn↗

arXiv2026

One-dimensional lattice random walks in a Gaussian random potential

We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random variables. We analyze three distinct models that specify how the transition rates depend on $U_x$: the random-force-like model, random walks with randomized stepping times, and the Gaussian trap model. Our analysis focuses on five key disorder-dependent quantities defined for a finite chain with $N$ sites: the probability current, its reciprocal (the resistance), the splitting probability $E_-$, the mean first-passage time $T_N$, and the diffusion coefficient $D_N$ in a periodic chain. By determining the moments of these random variables, we demonstrate that the probability current and resistance are not self-averaging, which leads to pronounced differences between their average and typical behaviors. In contrast, $E_-$, $T_N$ and $D_N$ become self-averaging when $N \to \infty$, though they exhibit strong sample-to-sample fluctuations for finite $N$.

cond-mat.stat-mech↗

arXiv2026

Inferring Concepts from Noisy Examples in Hopfield-like Neural Networks

We study a variant of the pseudo-inverse learning rule for Hopfield-like Neural Networks, which allows the network to infer archetypal concepts on the basis of a limited number of examples. The mean-field replica theory for this model reveals how this generalization ability is mediated by a multitude of states, with diverse thermodynamic properties, coexisting with the standard Hopfield ones. They appear and vanish through smooth transitions or discontinuous jumps and, interestingly, show much stronger Replica Symmetry Breaking (RSB) effects than the standard Hopfield model, as captured by our 1RSB analysis. Our results, in excellent agreement with numerical simulations, provide deeper insight into the interplay between memory storage and generalization in attractor neural networks.

cond-mat.dis-nn↗

arXiv2025

Paradoxical increase of capacity due to spurious overlaps in attractor networks

In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be hampered by overlaps between the network state and other memories, termed spurious overlaps since these overlaps collectively introduce noise in the retrieval process. In classic models, spurious overlaps increase the variance of synaptic inputs but do not affect the mean. We show here that in models equipped with a learning rule inferred from neurobiological data, spurious overlaps collectively reduce the mean synaptic inputs to neurons, and that this mean reduction causes in turn an increase in storage capacity through a sparsening of network activity. Our paper demonstrates a link between a specific feature of experimentally inferred plasticity rules and network storage capacity.

q-bio.NC↗

arXiv2025

Discrete-space and -time analogue of a super-diffusive fractional Brownian motion

We discuss how to construct reliably well "a lattice and an integer time" version of a super-diffusive continuous-space and -time fractional Brownian motion (fBm) -- an experimentally-relevant non-Markovian Gaussian stochastic process with an everlasting power-law memory on the time-evolution of thermal noises extending over the entire past. We propose two algorithms, which are both validated by extensive numerical simulations showing that the ensuing lattice random walks have not only the same power-law covariance function as the standard fBm, but also individual trajectories follow those of the super-diffusive fBm. Finding a lattice and an integer time analogue of a sub-diffusion fBm, which is an anti-persistent process, remains a challenging open problem. Our results also clarify the relevant difference between sub-diffusive and super-diffusive fBm, that are frequently seen as two very analogous realizations of processes with memory. They are indeed substantially different.

cond-mat.stat-mech↗

arXiv2025

A Very Effective and Simple Diffusion Reconstruction for the Diluted Ising Model

Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years, they have become extremely successful in generating multimedia content. However, it is still unknown if such models can be used to generate high-quality datasets of physical models. In this work, we use a Landau-Ginzburg-like diffusion model to infer the distribution of a $2D$ bond-diluted Ising model. Our approach is simple and effective, and we show that the generated samples reproduce correctly the statistical and critical properties of the physical model.

cond-mat.dis-nn↗

arXiv2025

A simple model of a sequence-reading diffusion: non-self-averaging and self-averaging properties

Motivated by a question about the sensitivity of knots' diffusive motion to the actual sequence of nucleotides placed on a given DNA, here we study a simple model of a sequence-reading diffusion on a stretched chain with a frozen sequence of "letters" $A$ and $B$, having different interaction energies. The chain contains a single distortion - a hernia - which brings the two letters at its bottom together such that they interact. Due to interactions with the solvent, the hernia performs a random hopping motion along the chain with the transition rates dependent on its actual position. Our two focal questions are a) the dependence of various transport properties on the letters' interaction energy and b) whether these properties are self-averaging with respect to different realizations of sequences. We show that the current through a finite interval, the resistance of this interval and the splitting probabilities on this interval lack self-averaging. On the contrary, the mean first-passage time through a finite interval with $N$ sites and the diffusion coefficient in a periodic chain are self-averaging in the limit $N \to \infty$. Concurrently, two latter properties exhibit sample-to-sample fluctuations for finite $N$, as evidenced by numerical simulations.

cond-mat.stat-mech↗

arXiv2023

Eigenvector Dreaming

Among the performance-enhancing procedures for Hopfield-type networks that implement associative memory, Hebbian Unlearning (or dreaming) strikes for its simplicity and its clear biological interpretation. Yet, it does not easily lend itself to a clear analytical understanding. Here we show how Hebbian Unlearning can be effectively described in terms of a simple evolution of the spectrum and the eigenvectors of the coupling matrix. We use these ideas to design new dreaming algorithms that are effective from a computational point of view, and are analytically far more transparent than the original scheme.

cond-mat.dis-nn↗

arXiv2022

Towards a robust criterion of anomalous diffusion

Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian -- or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.

cond-mat.stat-mech↗

arXiv2022

Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

We investigate the stochastic behavior of the single-trajectory spectral density $S(ω,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $ω$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(ω,\mathcal{T})$ for different values of $ω$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.

cond-mat.stat-mech↗

arXiv2022

Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

We discuss the statistical properties of a single-trajectory power spectral density $S(ω,\mathcal{T})$ of an arbitrary real-valued centered Gaussian process $X(t)$, where $ω$ is the angular frequency and $\mathcal{T}$ the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of $S(ω,\mathcal{T})$. Our findings imply that the fluctuations of $S(ω,\mathcal{T})$ exceed its average value $μ(ω,\mathcal{T})$. This implies that using $μ(ω,\mathcal{T})$ to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of $S(ω,\mathcal{T})$ and find that it deviates markedly from the average $μ(ω,\mathcal{T})$ in most cases.

cond-mat.stat-mech↗

arXiv2022

Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks

The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We analyze the stability of the stored memories: basins of attraction obtained by the Hebbian unlearning technique are found to be comparable in size to those obtained in the symmetric perceptron, while the two algorithms are found to converge in the same region of Gardner's space of interactions, having followed similar learning paths. A geometric interpretation of Hebbian unlearning is proposed to explain its optimal performances. Because the Hopfield model is also a prototypical model of disordered magnetic system, it might be possible to translate our results to other models of interest for memory storage in materials.

cond-mat.dis-nn↗

arXiv2021

Recognition Capabilities of a Hopfield Model with Auxiliary Hidden Neurons

We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero-temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly in a regime of complete confusion when memory load exceeds a sharp threshold.

cond-mat.dis-nn↗