TY - JOUR
T1 - Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature
T2 - The Perturbative Regime
AU - Arous, Gérard Ben
AU - Subag, Eliran
AU - Zeitouni, Ofer
PY - 2020/8/1
Y1 - 2020/8/1
N2 - We study the Gibbs measure of mixed spherical p-spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius (Formula presented.), where (Formula presented.) is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models.
AB - We study the Gibbs measure of mixed spherical p-spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius (Formula presented.), where (Formula presented.) is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models.
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U2 - 10.1002/cpa.21875
DO - 10.1002/cpa.21875
M3 - Article
AN - SCOPUS:85075461156
VL - 73
SP - 1732
EP - 1828
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 8
ER -