Zohar Nussinov

Limited resources motivate decomposing large-scale problems into smaller, “local” subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of “local hardness,” i.e., the complexity of predicting local properties of the solution from local information, for the ground-state problem of both P- and NP-hard spin glasses and related frustrated spin systems. Depending on the model considered, we observe varying scaling behaviors in how errors associated with local predictions decay as a function of the size of the solved subsystem. These errors are intimately connected to global critical threshold instabilities, characterized by gapless, avalanchelike excitations that follow scale-invariant size distributions. Away from criticality, local solvers quickly achieve high accuracy, aligning closely with the results of the computationally much more expensive global minimization. We leverage these findings to introduce a heuristic contraction-based algorithm for globally studying spin-glass ground states. The local solvers further display sharp imprints of the phase transition from the spin-glass to the ferromagnetic phase as the distribution of spin-glass couplings is shifted, as well as characteristic differences for the infinite-range model, implying the existence of specific classes of local hardness. Our findings shed light on how nature may operate solely through local actions at her disposal.

Unconventional superconductivity remains one of the central unsolved problems in quantum materials, and revealing its connection to the normal state is widely believed to be key to uncovering the pairing mechanism. Previous efforts have largely focused on the temperature range immediately above the superconducting transition, where specific scattering channels—such as strange-metal transport—have been identified as sharing a possible microscopic origin with superconductivity. Here, we use machine learning to explore possible correlations between normal-state resistivity and superconductivity in Fe-based compounds. We find that resistivity data in the temperature window of 150–300 K, far above the typical critical temperature ( T c ) of this family, can be used to classify whether a compound becomes superconducting. Owing to the limited size of the dataset, the underlying physical origin of this correlation cannot yet be determined. Nevertheless, the results suggest that high-temperature resistivity may contain useful empirical information for superconductivity prediction, motivating larger and more systematic experimental datasets.

Many complex physical systems admit natural decomposition into an exactly solvable component and a perturbative correction. Rather than training neural networks to learn complete trajectories from scratch, we introduce Neural Network Perturbation Theory (NNPT), where networks predict only residual perturbations after analytically subtracting known exact solutions. We validate this framework through systematic comparison: using identical 2x32 architectures, correction learning achieves 28-54x lower validation error compared to networks trained on complete trajectories. Using the gravitational three-body problem as a test bed, we investigate capacity transitions in fixed-architecture multilayer perceptrons as Jovian mass varies from 0.05 to 30 times its physical value. An equalized-accuracy protocol reveals that both minimal network capacity and training time exhibit sharp transitions at f_c = 15.6+-1.0, where the system enters a strongly chaotic regime. At this transition, minimal capacity jumps approximately sevenfold from ~1,200 to ~8,600 parameters (architectures 2x32 and 3x64). Preliminary exploration of sequential two-stage corrections suggests that first-stage networks already capture dominant perturbative features. Our symplectic integrator maintains relative energy conservation below 2x10^-7 throughout, confirming that transitions reflect physical complexity rather than numerical error. Our results establish correction learning as a general strategy for parameter-efficient surrogates and demonstrate that physical complexity imposes fundamental capacity barriers on fixed-architecture networks at chaos onset.

The phase diagram of QCD probably exhibits a moat regime over a large region of temperature T and chemical potential μ ≠ 0 . A moat regime is characterized by quasiparticle (pions) whose energy is minimal at nonzero spatial momentum. At μ ≠ 0 , higher mass dimension operators play a critical role in a moat regime. At dimension six, there are nine possible gauge-invariant couplings between scalars and photons. For back-to-back dilepton production, only one operator contributes, which significantly enhances production near a moat threshold. This enhancement is an experimental signature of moatons.

We introduce ``local uncertainty relations'' in thermal many-body systems, from which fundamental bounds in quantum systems can be derived. These lead to universal non-relativistic speed limits (independent of interaction range) and transport coefficient bounds (e.g., those of the diffusion constant and viscosity) that are compared against experimental data.

Systems displaying topological quantum order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and present a rich class of models exhibiting topological orders with distance-dependent interactions between anyons. As we illustrate, in some instances, . This leads to behaviors not typically described by topological quantum field theories. We examine these models by performing exact dualities to systems displaying conventional (i.e., Landau) orders. Our approach enables a general method for mapping Landau-type theories to dual models with topological order, while preserving the same spatial dimension. The low-energy subspaces of our models can be made more resilient to thermal effects than those of surface codes. Published by the American Physical Society 2025

We consider the effect of perturbing a single bond on ground states of nearest-neighbor Ising spin glasses, with a Gaussian distribution of the coupling constants, across various two- and three-dimensional lattices and regular random graphs. Our results reveal that the ground states are strikingly fragile with respect to such changes. Altering the strength of only a single bond beyond a critical threshold value leads to a new ground state that differs from the original one by a droplet of flipped spins whose boundary and volume diverge with the system size—an effect that is reminiscent of the more familiar phenomenon of disorder chaos. These elementary fractal-boundary zero-energy droplets and their composites feature robust characteristics and provide the lowest-energy macroscopic spin-glass excitations. Remarkably, within numerical accuracy, the size of such droplets conforms to a universal power-law distribution with exponents that depend on the spatial dimension of the system. Furthermore, the critical coupling strengths adhere to a stretched exponential distribution that is predominantly determined by the local coordination number.