Spin-glass chaos with Boolean Fourier analysis
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. ...