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# Ising Model

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arXiv Nov 9, 2026
Path integral diffusion picks a mirror half first, then settles glassy classes in one compound decision
When path integral diffusion (PID) generates a finite Ising spin glass from a point source, each trajectory first chooses one of the two mirror halves of the zero-field measure, then decides among glassy classes inside that half. Theory shows every isotropic PID is Gaussian stochastic localization seen on a different clock, so the protocol sets when decisions happen and what they cost, not what is decided; on exactly enumerable Bethe and SK glasses, nested glassy levels are often settled in one or two distinct events, and these classes appear near the glass transition, keep their identity on cooling, and are absent in a ferromagnet on the same graphs.
When path integral diffusion (PID) generates a finite Ising spin glass from a point source, each trajectory first chooses one of the two mirror halves of the zero-field measure, then decides among glassy classes inside that half. Theory shows every isotropic PID is Gaussian stochastic localization seen on a different clock, so the protocol sets when decisions happen and what they cost, not what is decided; on exactly enumerable Bethe and SK glasses, nested glassy levels are often settled in one or two distinct events, and these classes appear near the glass transition, keep their identity on cooling, and are absent in a ferromagnet on the same graphs.
Michael Chertkov（First author, Corresponding author）
Path Integral Diffusion Stochastic localization Spin glass Speciation decision times in diffusion sampling Ising Model
arXiv Nov 4, 2026
Putting an Ising model inside a hidden Markov chain: pseudolikelihood sidesteps the partition function, and U.S. county gun-death weeks split into four states
The hidden Markov Ising model makes an Ising model, a binary graphical model from statistical physics, the emission distribution of a hidden Markov chain, so that a binary network's dependence structure is modeled directly as its state changes over time. Because the Ising normalizing constant grows exponentially with the number of nodes, fitting uses pseudolikelihood inside Baum-Welch reestimation, with results on the algorithm's validity, model identifiability and large-network consistency. Exogenous covariates extend it to a hidden Markov autologistic model, applied to a five-year sequence of weekly gun-death events across 3109 continental U.S. counties from 2021 to 2025, where it identifies state changes in gun violence activity.
The hidden Markov Ising model makes an Ising model, a binary graphical model from statistical physics, the emission distribution of a hidden Markov chain, so that a binary network's dependence structure is modeled directly as its state changes over time. Because the Ising normalizing constant grows exponentially with the number of nodes, fitting uses pseudolikelihood inside Baum-Welch reestimation, with results on the algorithm's validity, model identifiability and large-network consistency. Exogenous covariates extend it to a hidden Markov autologistic model, applied to a five-year sequence of weekly gun-death events across 3109 continental U.S. counties from 2021 to 2025, where it identifies state changes in gun violence activity.
University of Alberta
Aari Vinayagasothy（First author）
Hidden Markov Ising Model Ising Model Maximum Pseudolikelihood Estimation Baum-Welch Algorithm Hidden Markov Model

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