TY - JOUR

T1 - The Generalized TAP Free Energy II

AU - Chen, Wei Kuo

AU - Panchenko, Dmitry

AU - Subag, Eliran

N1 - Funding Information:
W. Chen: Partially supported by NSF grant DMS-17-52184.
Funding Information:
D. Panchenko: Partially supported by NSERC.
Funding Information:
E. Subag Supported by the Simons Foundation.

PY - 2020

Y1 - 2020

N2 - In a recent paper (Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math.), we developed the generalized TAP approach for mixed p-spin models with Ising spins at positive temperature. Here we extend these results in two directions. We find a simplified representation for the energy of the generalized TAP states in terms of the Parisi measure of the model and, in particular, show that the energy of all states at a given distance from the origin is the same. Furthermore, we prove the analogues of the positive temperature results at zero temperature, which concern the ground-state energy and the organization of ground-state configurations in space.

AB - In a recent paper (Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math.), we developed the generalized TAP approach for mixed p-spin models with Ising spins at positive temperature. Here we extend these results in two directions. We find a simplified representation for the energy of the generalized TAP states in terms of the Parisi measure of the model and, in particular, show that the energy of all states at a given distance from the origin is the same. Furthermore, we prove the analogues of the positive temperature results at zero temperature, which concern the ground-state energy and the organization of ground-state configurations in space.

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U2 - 10.1007/s00220-020-03887-x

DO - 10.1007/s00220-020-03887-x

M3 - Article

AN - SCOPUS:85095798837

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -