Spin-Glass

Change a small fraction of the bonds in a spin glass. How much of the spin configuration changes? For the fair ±J Edwards–Anderson model, there is a short answer using Fourier analysis on the Boolean cube. The decisive observation is geometric: every surviving Fourier term for a two-spin correlation must contain a path between those spins. The usual noise operator then suppresses it. This is an exposition of a known result. Chatterjee’s 2023 paper proved site-overlap disorder chaos at zero temperature for Gaussian couplings. Chen, Kim and Sen, first posted in 2024 and revised in 2025, extended the result to general symmetric disorder and all temperatures. Here is the fair-bimodal, bond-resampling specialization of their argument, written directly in the language of Boolean Fourier analysis. ...

Simulating spin glasses at scale has always been a pain — Python is too slow, and C++ is too painful. Peapods is my attempt at a middle ground: a Monte Carlo package for Ising spin systems where the hot loops are written in Rust and everything else stays in Python, glued together with PyO3. You just pip install peapods and go. ...

Unlike ferromagnetic spin models, a spin glass has a highly non-trivial phase transition profile. For mean field models (the SK spin glass), the glass experiences a replica-symmetry breaking phenomenon that is only fully understood recently. However, for short-range models, almost nothing is known rigorously, including basic problems such as the nature of the glass transition. A potential route towards settling such problems may rely on a suitable generalization of the random cluster model as a universal statistical tool. ...