TY - JOUR
T1 - On the TAP Equations via the Cavity Approach in the Generic Mixed p-Spin Models
AU - Chen, Wei Kuo
AU - Tang, Si
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/4
Y1 - 2024/4
N2 - In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington–Kirkpatrick (SK) spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections to Parisi’s replica ansatz. In this work, we aim to investigate the validity of the TAP equations in the generic mixed p-spin model. By utilizing the ultrametricity of the overlaps, we show that the TAP equations are asymptotically satisfied by the conditional local magnetizations on the asymptotic pure states.
AB - In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington–Kirkpatrick (SK) spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections to Parisi’s replica ansatz. In this work, we aim to investigate the validity of the TAP equations in the generic mixed p-spin model. By utilizing the ultrametricity of the overlaps, we show that the TAP equations are asymptotically satisfied by the conditional local magnetizations on the asymptotic pure states.
UR - http://www.scopus.com/inward/record.url?scp=85187952400&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85187952400&partnerID=8YFLogxK
U2 - 10.1007/s00220-024-04971-2
DO - 10.1007/s00220-024-04971-2
M3 - Article
AN - SCOPUS:85187952400
SN - 0010-3616
VL - 405
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 4
M1 - 87
ER -