Spin glasses – systems with disordered magnetic interactions – serve as a fundamental model for studying complexity in physics. While their behavior is well characterized in Fully Connected (i.e., infinite-dimensional) systems, a Comprehensive theory for real-world spin glasses remains elusive. In particular, although the existence of a phase transition under a magnetic field is firmly established in infinite dimensions, its presence in finite dimensions remains controversial. In this article we introduce an approach based on the Bethe approximation (an advanced mean-field framework) to demonstrate that spin glasses indeed undergo a transition into a frozen, disordered phase even in finite-dimensional systems.
Furthermore, our method provides quantitative predictions for critical properties near this transition.
 

Articolo:
M.C. Angelini,S. Palazzi,G. Parisi, & T. Rizzo,  Critical exponents of the spin-glass transition in a field at zero temperature, Proc. Natl. Acad. Sci. U.S.A. 122 (37) e2511882122, https://doi.org/10.1073/pnas.2511882122  (2025)