无序系统与神经网络

Spin-glass models of associative memories are a cornerstone between statistical physics and theoretical neuroscience. In these networks, stochastic spin-like units interact through a synaptic matrix shaped by local Hebbian learning. In…

The non-Hermitian skin effect is the accumulation of eigenstates at the boundaries, reflecting the system's nonreciprocity. Introducing disorder leads to a competition between the skin effect and Anderson localization, giving rise to the…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…

It is now established that glasses feature low-frequency, nonphononic excitations, in addition to phonons that follow Debye's vibrational density of state (VDoS). Extensive computer studies demonstrated that these nonphononic, glassy…

We construct the first complete exact numerical solution of a mean field quantum spin glass model, the transverse field Sherrington-Kirkpatrick model, by implementing a continuous-time quantum Monte Carlo method in the presence of full…

We study the Coulomb glass emerging from the interplay of strong interactions and disorder in a model of spinless fermions on the Bethe lattice. In the infinite coordination number limit, strong interactions induce a metallic Coulomb glass…

In this study, we investigate Anderson localization in a one-dimensional lattice with a mosaic off-diagonal quasiperiodic hopping. Our findings reveal that the localization behavior of zero-energy states is highly dependent on the parity of…

Seemingly identical Bulk Metallic Glasses (BMG) often exhibit strikingly different mechanical properties despite having the same composition and fictive temperature. A postulated mechanism underlying these differences is the presence of…

We study the phases and phase transitions of a disordered one-dimensional quantum $q$-state clock Hamiltonian using large-scale Monte Carlo simulations. Making contact with earlier results, we confirm that the clean, translational invariant…

Phase transitions are prevalent throughout physics, spanning thermal phenomena like water boiling to magnetic transitions in solids. They encompass cosmological phase transitions in the early universe and the transition into a quark-gluon…

We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite-width two-layer neural network with non-overlapping…

We study the binary symmetric perceptron model, and in particular its atypical solutions. While the solution-space of this problem is dominated by isolated configurations, it is also solvable for a certain range of constraint density…

We map the problem of determining flat-foldability of the origami diagram onto the ground-state search problem of spin glass model on random graphs. If the origami diagram is locally flat-foldable around each vertex, a pre-folded diagram,…

This study introduces a physics-informed machine learning framework to accelerate the computation of the microkinetic model of Fischer-Tropsch synthesis. A neural network, trained within the NVIDIA Modulus framework, approximates the…

We investigate the phase transitions in a one-dimensional system with colored noise. Previous studies indicated that the phase diagram of this system included extended and disorder-induced localized phases. However, by studying the…

We investigate the distance from equilibrium using the Kuramoto model via the degree of fluctuation-dissipation violation as the consequence of different levels of edge weight anisotropies. This is achieved by solving the synchronization…

The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable results, such as the celebrated elliptic law for dense random…

This work introduces a generic quantitative framework for studying dynamical processes that involve interactions of polymer sequences. Possible applications range from quantitative studies of the reaction kinetics of polymerization…

Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to…