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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles Almeida-Thouless transition below six dimensions Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses Probing the Almeida-Thouless line away from the mean-field model The de Almeida-Thouless line in vector spin glasses Disappearance of the de Almeida-Thouless line in six dimensions The 1/m expansion in spin glasses and the de Almeida-Thouless line Evidence against an Almeida-Thouless line in disordered systems of Ising dipoles Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean field spin glass mode The replica symmetric region in the Sherrington-Kirkpatrick mean field spin glass model. The Almeida-Thouless line More... Physics 2010 # Finite size scaling of the de Almeida-Thouless instability in random sparse networks  Full-Text Cite this paper Abstract: We study, in random sparse networks, finite size scaling of the spin glass susceptibility$\chi_{\rm SG}$, which is a proper measure of the de Almeida-Thouless (AT) instability of spin glass systems. Using a phenomenological argument regarding the band edge behavior of the Hessian eigenvalue distribution, we discuss how$\chi_{\rm SG}$is evaluated in infinitely large random sparse networks, which are usually identified with Bethe trees, and how it should be corrected in finite systems. In the high temperature region, data of extensive numerical experiments are generally in good agreement with the theoretical values of$\chi_{\rm SG}$determined from the Bethe tree. In the absence of external fields, the data also show a scaling relation$\chi_{\rm SG}=N^{1/3}F(N^{1/3}|T-T_c|/T_c)$, which has been conjectured in the literature, where$T_c\$ is the critical temperature. In the presence of external fields, on the other hand, the numerical data are not consistent with this scaling relation. A numerical analysis of Hessian eigenvalues implies that strong finite size corrections of the lower band edge of the eigenvalue distribution, which seem relevant only in the presence of the fields, are a major source of inconsistency. This may be related to the known difficulty in using only numerical methods to detect the AT instability.

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