For large N the optimal dispersed subset consists of all points lying outside a self-consistently determined d-dimensional ball, with the entire distribution of maximal dispersion obtained via mean-field order statistics and the replica method.
Mean field theory of spin glasses
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abstract
These lecture notes focus on the mean field theory of spin glasses, with particular emphasis on the presence of a very large number of metastable states in these systems. This phenomenon, and some of its physical consequences, will be discussed in details for fully-connected models and for models defined on random lattices. This will be done using the replica and cavity methods. These notes have been prepared for a course of the PhD program in Statistical Mechanics at SISSA, Trieste and at the University of Rome "Sapienza". Part of the material is reprinted from other lecture notes, and when this is done a reference is obviously provided to the original.
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2026 2verdicts
UNVERDICTED 2representative citing papers
A 2D disordered O(N) sigma model at large N exhibits a low-temperature spin glass phase with finite Edwards-Anderson parameter and approximate scaling in the dynamical two-point function.
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The Most Dispersed Subset of Random Points in $\mathbb{R}^d$
For large N the optimal dispersed subset consists of all points lying outside a self-consistently determined d-dimensional ball, with the entire distribution of maximal dispersion obtained via mean-field order statistics and the replica method.
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The two-dimensional disordered $O(N)$ sigma model
A 2D disordered O(N) sigma model at large N exhibits a low-temperature spin glass phase with finite Edwards-Anderson parameter and approximate scaling in the dynamical two-point function.