The Jamming Transition

Altieri, Ada

doi:10.1007/978-3-030-23600-7_3

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2023

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“…In fact, theories based on disordered systems often reveal to be beneficial for the treatment of problems outside the domain of SGs. Heterogeneous systems, either with quenched or self-generated disorder, are much more general than it might be believed at first glance, ranging from neural networks and optimization problems [53,54,57,[187][188][189][190][191][192][193], signal reconstruction [194,195], random lasers [196,197], financial markets [198][199][200], supercooled liquids and jammed packings [201][202][203][204][205] and theoretical ecology [206][207][208][209][210][211][212][213][214], and thermodynamic and dynamic formalisms rooted in spin-glass theory can still be used to solve them.…”

Section: Discussionmentioning

confidence: 99%

An Introduction to the Theory of Spin Glasses

Altieri¹,

Baity‐Jesi²

2023

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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.

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