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Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses

幸徳外崎, 晃人竹田, Koujin Takeda +2 more

May 1, 20070 citations

Numerical study of the TAP equations for infinite-range spin glass models

Terufumi Yokota

Physica A Statistical Mechanics and its ApplicationsJun 1, 19920 citations

Numerical study of aging processes in the SK and 3D-EA Ising spin-glass models

Hajime Takayama, Hajime Yoshino, 達雄小森 +1 more

Journal of Magnetism and Magnetic MaterialsJan 1, 19982 citations

Free energy of the quantum Sherrington–Kirkpatrick spin-glass model with transverse field

Arka Adhikari, Christian Brennecke

We consider the quantum Sherrington–Kirkpatrick (SK) spin-glass model with a transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures β > 0. To characterize the free energy, we use the path integral representation of the partition function and approximate the model by a sequence of finite-dimensional vector-spin glasses with Rd-valued spins. This enables us to use the results of Panchenko who generalized [Ann. Probab. 46(2), 829–864 (2018); ibid, 46(2), 865–896 (2018)] the Parisi formula to classical vector-spin glasses. As a consequence, we can express the thermodynamic limit of the free energy of the quantum SK model as the d → ∞ limit of the free energies of the d-dimensional approximations of the model.We consider the quantum Sherrington–Kirkpatrick (SK) spin-glass model with a transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures β > 0. To characterize the free energy, we use the path integral representation of the partition function and approximate the model by a sequence of finite-dimensional vector-spin glasses with Rd-valued spins. This enables us to use the results of Panchenko who generalized [Ann. Probab. 46(2), 829–864 (2018); ibid, 46(2), 865–896 (2018)] the Parisi formula to classical vector-spin glasses. As a consequence, we can express the thermodynamic limit of the free energy of the quantum SK model as the d → ∞ limit of the free energies of the d-dimensional approximations of the model.

arXiv:1912.13041Journal of Mathematical PhysicsAug 1, 202011 citations

Modified TAP equations for the SK spin glass

T. Plefka, Theoretische Festkörperphysik Tu Darmstadt

PACS. 75.10.Nr – Spin-glass and other random models. PACS. 84.35.+i – Neural networks. Abstract. – The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed. Introduction. – Together with the replica approach, the Thouless-Anderson-Palmer (TAP) approach [1] is the most important method to analyze infinite range spin glass models like the Sherrington-Kirkpatrick (SK) model [2] of Ising spins (for reviews see [3, 4]). The TAP equations are well established [3–5] and are exact in the thermodynamic limit (N → ∞) provided that the local magnetizations {mi} satisfy the conditionPACS. 75.10.Nr – Spin-glass and other random models. PACS. 84.35.+i – Neural networks. Abstract. – The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed. Introduction. – Together with the replica approach, the Thouless-Anderson-Palmer (TAP) approach [1] is the most important method to analyze infinite range spin glass models like the Sherrington-Kirkpatrick (SK) model [2] of Ising spins (for reviews see [3, 4]). The TAP equations are well established [3–5] and are exact in the thermodynamic limit (N → ∞) provided that the local magnetizations {mi} satisfy the condition

Jan 1, 200211 citations

Numerical studies of spin glasses

R. N. Bhatt, A. P. Young

Lecture notes in physicsJan 1, 19873 citations

Structure of tap free energy surface of SK spin glasses (numerical study of pure states)

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