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Chapter 4: Renormalization Group in Spin Glasses

The renormalization group treatment of spin glasses has been a theoretical challenge since shortly after the formulation of the Sherrington–Kirkpatrick model.

This chapter brings three perspectives on this topic. Section 4.1, by T. Lubensky, reviews the early replica symmetric description of the problem, which predate and in some ways anticipate the discovery of the instability of that treatment by de Almeida and Thouless.

The perturbative renormalization group approach to the ensuing transition is presented in Sec. 4.2, contributed jointly by T. Temesvari and I. Kondor. The findings of this approach motivate the consideration of non-perturbative renormalization group schemes, which are discussed in Sec. 4.3 written by M. C. Angelini.

T. Lubensky, T. Temesvari, I. Kondor, M.C. Angelini, Chapter 4: Renormalization Group in Spin Glasses, In: Charbonneau, P.; Marinari, E.; Mezard, M.; Parisi, G.; Ricci-Tersenghi, F.; Sicuro, G.; Zamponi, F.; Spin Glass Theory and Far Beyond: Replica Symmetry Breaking after 40 Years, (2023) 45-67..

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