An Introduction to the Theory of Spin Glasses

Abstract

We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method, and the dynamical mean-field theory. In the second part, we deal with the description of low-dimensional systems, mostly in three spatial dimensions, which are mostly studied through numerical simulations. We conclude by mentioning some of the main open problems in the field.

arXiv commentTo appear as a chapter of the "Encyclopedia of Condensed Matter Physics", 2nd edition (Elsevier)

References in corpus (1)

• Spin-Glass Theory for Pedestrians

Cited by in corpus (2)

• A near-term quantum simulation of the transverse field Ising model hints at Glassy Dynamics
• Microbiomes Through The Looking Glass: Linking species interactions to dysbiosis through a disordered Lotka-Volterra framework