Ising Model

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The Ising model represents systems of binary spins whose pairwise couplings and external fields determine their energy or probability, making it a basic setting for studying magnetism and phase transitions. Researchers use tools such as Monte Carlo sampling, pseudolikelihood estimation, graphical-model methods, and neural or quantum samplers to analyze these systems. Ising models also provide useful frameworks for network interventions, causal inference, machine learning, and combinatorial optimization. A central challenge is that efficient learning and sampling depend strongly on interaction structure and temperature: methods can work well in tractable regimes, while nearby regimes may be computationally hard.

Latest papers

13 papers0 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

High-Magnetization Sampling at Low Temperatures: Ising Models and Bayesian Sparse Linear Regression
Sep 8, 2026Syamantak Kumar, Purnamrita Sarkar, Kevin Tian +1Sparse Recovery Ising Model
University of Texas at Austin
Data Driven Equation Discovery for Phase-Ordering Dynamics : From Allen Cahn to the Ising Model
Aug 4, 2026Partha Sarathi Mondal, Manav Kumar Jalan, Anish Kumar +1Sparse Identification of Nonlinear Dynamics PDE Discovery
Department of Physics, Indian Institute of Technology (BHU) Varanasi, India 221005
Practical advantage beyond the quadratic speedup limit with fully-quantum walks
Jul 24, 2026Massimiliano Incudini, Guglielmo MazzolaMarkov Chain Monte Carlo Ising Model
International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy
Causal Inference for Sequential Settings under Interference and Latent Confounding
Jul 16, 2026Phevos Paschalidis, Constantinos Daskalakis, Devavrat ShahCausal Effect Estimation Causal Inference with Unobserved Confounding
EECS, LIDS, CSAIL · MIT · EECS, CSAIL +1
Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model
Jul 11, 2026Max Weinmann, Miriam KlopotekAutoencoders Unsupervised Representation Learning
1WIN-Kolleg of the Young Academy | Heidelberg Academy of Sciences and Humanities, Karlstraße 4, 69117 Heidelberg, Germany · 2Stuttgart Center for Simulation Science, Cluster of Excellence EXC 2075, University of Stuttgart, Universitätsstraße 32, 70569 Stuttgart, Germany
Transfer Learning in High-dimensional Ising Models
Jul 3, 2026Joonho Kim, Seyoung ParkGraph Structure Learning Ising Model
Kim Jaechul Graduate School of Artificial Intelligence, KAIST, Seoul, Republic of Korea · Department of Statistics and Data Science, Yonsei University, Seoul, Republic of Korea
Energy-efficient codon optimization on thermodynamic hardware
Jun 15, 2026Andraz Jelincic, Ross C. WalkerThermodynamic Computing Ising Model
1Extropic Corp., Boston, MA
Boltzmann Attention: Learnable Ising Couplings for Cooperative Attention
Jun 10, 2026Gilhan Kim, Daniel K. ParkQuantum Annealing Ising Model
Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea · Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea · Department of Quantum Information, Yonsei University, Seoul 03722, Republic of Korea
A computational phase transition for learning-to-sample from Ising models
May 23, 2026Andrej Risteski, Thuy-Duong VuongPhase Transitions Ising Model
Machine Learning Department, Carnegie Mellon University. · Department of Computer Science and Engineering, UC San Diego.
Dynamic Treatment on Networks
May 7, 2026Bengusu Nar, Jiguang Li, Veronika Ročková +1Sequential Decision Making Ising Model
Econometrics and Statistics at the Booth School of Business of the University of Chicago · Bruce Lindsay Professor of Econometrics and Statistics in the Wallman Society of Fellows at the Booth School of Business of the University of Chicago · Professor of Econometrics and Statistics, and John E. Jeuck Faculty Fellow at the Booth School of Business of the University of Chicago
Joint Consistency: A Unified Test-Time Aggregation Framework via Energy Minimization
May 7, 2026Yunzhen Yao, Hongye Wang, Yahong Wang +3Ising Model
EPFL · SUFE
Sampling two-dimensional spin systems with transformers
Apr 30, 2026Piotr Białas, Piotr Korcyl, Tomasz Stebel +2Transformer Ising Model
Institute of Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland · Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland · Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
Selecting Optimal Variable Order in Autoregressive Ising Models
Feb 23, 2026Shiba Biswal, Marc Vuffray, Andrey Y. LokhovAutoregressive Modeling Ising Model
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545.

Sep 8, 2026J/K move · Enter open · S save

High-Magnetization Sampling at Low Temperatures: Ising Models and Bayesian Sparse Linear Regression

Syamantak Kumar, Purnamrita Sarkar, Kevin Tian, Yusong Zhu

University of Texas at Austin

Sparse Recovery Ising Model Posterior Sampling

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Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over the Hamming slice

\mathcal{X}_k^d:=\{\mathbf{x}\in\{\pm 1\}^d:|\{i:\mathbf{x}_i=1\}|=k\}

, in high-dimensional regimes where

k\ll d

(i.e., where

\mathcal{X}_k^d

is highly magnetized). We use our frameworks to design improved samplers for canonical problems in the study of Ising models and Bayesian sparse linear regression. Our first main result considers the Sherrington--Kirkpatrick (SK) model restricted to fixed-magnetization slices

\mathcal{X}_k^d

. We give a polynomial-time sampler for fixed-magnetization SK models at any inverse temperature

β>0

, under arbitrary external fields, provided that

k\le c_βd

for an appropriate constant

c_β

. By combining this result with an annealing strategy for estimating normalizing constants, we obtain polynomial-time samplers for the SK model at arbitrarily low temperatures under a sufficiently strong external field of strength

h

. In the large-

β

limit, our framework permits sampling at field strengths within constant factors of the Almeida--Thouless line delineating the replica-symmetric and replica-symmetry-breaking regions ([dAT78]), improving polynomially over the field strength

h(β)

required by the recent work of [BAR26]. Our second main result concerns the measurement complexity of polynomial-time Bayesian sparse linear regression. Recent work by [KSTZ25] shows how to sample from the canonical Gaussian spike-and-slab posterior with expected sparsity

k

, at any signal-to-noise ratio, given

n\gtrsim k^3\log^3 d

Gaussian measurements. We improve this requirement to

n\gtrsim k^{3/2}\log^2 d+k\log^3 d

, using a common sparsity-aware framework underlying both our results.