The Complexity of Vector Spin Glasses

Abstract

We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of positive eigenvalues in addition to an isolated eigenvalue and (m-1) null eigenvalues due to rotational invariance. Rather surprisingly, the band does not extend to zero at any finite temperature. The isolated eigenvalue becomes zero in the thermodynamic limit, as in the Ising case (m=1), indicating that the same supersymmetry breaking recently found in Ising spin glasses occurs in vector spin glasses.

4 pages, 2 figures

References in corpus (10)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• The Complexity of Ising Spin Glasses
• On the formal equivalence of the TAP and thermodynamic methods in the SK model
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• Numerical study of metastable states in Ising spin glasses
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• Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation
• On Spin-Glass Complexity
• The role of the Becchi-Rouet-Stora-Tyutin supersymmetry in the calculation of the complexity for the Sherrington-Kirkpatrick model

Cited by in corpus (4)

• The metastable minima of the Heisenberg spin glass in a random magnetic field
• Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas
• Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses
• The m-component spin glass on a Bethe lattice