Phase Transitions

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Phase-transition research studies how many interacting parts can shift together from one kind of behavior to another, and why these changes matter for predicting material properties, collective dynamics, and learning systems. Researchers use order parameters, susceptibility, finite-size scaling, and renormalization-group methods to locate critical points and test whether different systems share universal behavior. Neural networks, active learning, persistent homology, and physics-informed simulators extend these tools to settings such as Ising and percolation models, quantum systems, and training dynamics. A central challenge is distinguishing genuine critical transitions from smooth crossovers or finite-size effects, especially in noisy, non-equilibrium systems where standard equilibrium theory may not apply.

Latest papers

69 papers6 papers in the last four weeks, up 100% on the four weeks before. 0.0% of all new papers.

Spectral Edge Dynamics: An Analytical-Empirical Study of Phase Transitions in Neural Network Training
Mar 30, 2026Yongzhong XuPhase Transitions in Neural Networks Neural Network Training Dynamics
Grokking as a Falsifiable Finite-Size Transition
Mar 25, 2026Yuda Bi, Chenyu Zhang, Qiheng Wang +1Grokking Phase Transitions
Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS Center), Atlanta, Georgia 30303, USA · Beijing Institute of Technology, Beijing 100081, China · Georgia Institute of Technology, Atlanta, Georgia 30332, USA
Optimal Scalar Quantization for Matrix Multiplication: Closed-Form Density and Phase Transition
Mar 20, 2026Calvin Ang, Sungyoon Kim, Mert PilanciNeural Network Quantization Activation Quantization
Stanford University
AI-Driven Phase Identification from X-ray Hyperspectral Imaging of cycled Na-ion Cathode Materials
Mar 8, 2026Fayçal Adrar, Nicolas Folastre, Chloé Pablos +7Materials Science Phase Transitions
Laboratoire de Réactivité et de Chimie des Solides (LRCS), CNRS UMR 7314, Université de Picardie Jules Verne, Hub de l’Energie, 15 Rue Baudelocque, Amiens, France · Réseau sur le Stockage Electrochimique de l’Energie (RS2E), CNRS FR 3459, Hub de l’Energie, 15 Rue Baudelocque, Amiens, France · ALISTORE-European Research Institute, CNRS FR 3104, Hub de l’Energie, Rue Baudelocque, Amiens, France +3
Unsupervised Discovery of Intermediate Phase Order in the Frustrated $J_1$ - $J_2$ Heisenberg Model via Prometheus Framework
Feb 25, 2026Brandon Yee, Wilson Collins, Maximilian RutkowskiPhase Transitions Quantum Many-Body Physics
Physics Lab, Yee Collins Research Group
From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems
Feb 16, 2026Brandon Yee, Wilson Collins, Pairie Koh +1Phase Transitions Quantum Many-Body Physics
Physics Lab, Yee Collins Research Group
Persistent Entropy as a Detector of Phase Transitions
Feb 8, 2026Marcos Gutierrez-del-Pozo, Eduardo Paluzo-Hidalgo, Matteo RuccoPhase Transitions Persistent Homology
Emergent interactions lead to collective frustration in robotic matter
Jul 29, 2025Onurcan Bektas, Adolfo Alsina, Steffen RulandsPhase Transitions Multi-Agent Systems
Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoSciences, Ludwig-Maximilians-Universität München, Theresienstr. 37, München, 80333, Germany. · Max-Planck-Institute for the Physics of Complex Systems, Noethnitzer Str. 38, Dresden, 01187, Germany. · GISC, Universidad Rey Juan Carlos, c/ Tulip´an s/n, 28933, M´ostoles, Spain.
Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models
Jul 5, 2025Shanshan Wang, Dian Xu, Jianmin Shen +3Phase Transitions Siamese Neural Networks
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, , Wuhan, 430079, Hubei, China · School of Engineering and Technology, Baoshan University, , Baoshan, 678000, Yunnan, China · Ecole Superieure d’Informatique Electronique Automatique, , Ivry-sur-Seine, 94200, , France

Mar 30, 2026J/K move · Enter open · S save

Spectral Edge Dynamics: An Analytical-Empirical Study of Phase Transitions in Neural Network Training

Yongzhong Xu

Phase Transitions in Neural Networks Neural Network Training Dynamics Phase Transitions Grokking

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We develop the spectral edge analysis: phase transitions in neural network training -- grokking, capability gains, loss plateaus -- are controlled by the spectral gap of the rolling-window Gram matrix of parameter updates. In the extreme aspect ratio regime (parameters

P \sim 10^8

, window

W \sim 10

), the classical BBP detection threshold is vacuous; the operative structure is the intra-signal gap separating dominant from subdominant modes at position

k^* = \mathrm{argmax}\, σ_j/σ_{j+1}

. From three assumptions we derive: (i) gap dynamics governed by a Dyson-type ODE with curvature asymmetry, damping, and gradient driving; (ii) a spectral loss decomposition linking each mode's learning contribution to its Davis--Kahan stability coefficient; (iii) the Gap Maximality Principle, showing that

k^*

is the unique dynamically privileged position -- its collapse is the only one that disrupts learning, and it sustains itself through an

α

-feedback loop requiring no assumption on the optimizer. The adiabatic parameter

\mathcal{A} = \|ΔG\|_F / (η\, g^2)

controls circuit stability:

\mathcal{A} \ll 1

(plateau),

\mathcal{A} \sim 1

(phase transition),

\mathcal{A} \gg 1

(forgetting). Tested across six model families (150K--124M parameters): gap dynamics precede every grokking event (24/24 with weight decay, 1/24 without), the gap position is optimizer-dependent (Muon:

k^*=1

, AdamW:

k^*=2

on the same model), and 19/20 quantitative predictions are confirmed. The framework is consistent with the edge of stability, Tensor Programs, Dyson Brownian motion, the Lottery Ticket Hypothesis, and neural scaling laws.