无序系统与神经网络：2025–2026 年度综述

An annual survey of the cond-mat.dis-nn arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 108 papers and organised into 40 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• Many-Body Localization and Topological Transport Dynamics (73.7%) — Investigates long-time dynamics, entanglement transitions, and topological phases in disordered quantum systems, focusing on MBL and transport phenomena.
• Anderson Localization in Random Graphs and Non-Hermitian Systems (11.0%) — Explores localization mechanisms in spatially structured random graphs, non-Hermitian skin modes, and spectral properties of disordered lattices.
• Quantum Spin Glasses and Neural Quantum State Representations (6.6%) — Studies ground states and excitations of quantum spin glasses while developing neural network-based wavefunction ansatzes for efficient simulation.
• Dynamical Mean-Field Theory and Glassy Structural Dynamics (2.4%) — Applies dynamical mean-field theory and cavity methods to understand relaxation mechanisms and structural properties in glasses and oscillator networks.
• Energy Landscapes and Training Dynamics in Neural Networks (2.3%) — Analyzes the geometry of energy and loss landscapes in machine learning models, linking ultrametricity and phase transitions to training performance.
• Critical Phenomena in Non-Hermitian and Measurement-Induced Transitions (1.8%) — Examines critical behavior and phase transitions in non-Hermitian quasicrystals and measurement-induced dynamics, focusing on universality classes.
• Combinatorial Optimization and Spin-Glass Solvers (1.2%) — Develops algorithms and hardware-inspired approaches, including QAOA and Ising machines, to solve hard combinatorial optimization problems.
• Scaling Limits and Learnability in Language and Network Models (0.5%) — Investigates the statistical mechanics of language models and network structures, addressing scaling limits and learnability of complex tasks.
• Emergent Dynamics in Complex Physical and Biological Systems (0.4%) — Addresses open theoretical challenges in understanding emergent order and relaxation in complex ecosystems, materials, and neural systems.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.