Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-04-07
Physics
Condensed Matter
Disordered Systems and Neural Networks
4 pages, 2 figures
Scientific paper
10.1103/PhysRevLett.93.077201
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.
Moore Anna M.
Yeo Joonhyun
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