We present a method derived by cavity arguments to compute the spin-glass and higher order susceptibilities in diluted mean-field spin-glass models. The divergence of the spin-glass susceptibility is associated with the existence of a non-zero solution of a homogeneous linear integral equation. Higher order susceptibilities, relevant for critical dynamics through the parameter exponent ?, can be expressed at criticality as integrals involving the critical eigenvector. The numerical evaluation of the corresponding analytic expressions is discussed. The method is illustrated in the context of the de Almeida-Thouless line for a spin glass on a Bethe lattice but can be generalized straightforwardly to more complex situations. © 2014 IOP Publishing Ltd and SISSA Medialab srl.
Diluted mean-field spin-glass models at criticality
Rizzo T
2014
Abstract
We present a method derived by cavity arguments to compute the spin-glass and higher order susceptibilities in diluted mean-field spin-glass models. The divergence of the spin-glass susceptibility is associated with the existence of a non-zero solution of a homogeneous linear integral equation. Higher order susceptibilities, relevant for critical dynamics through the parameter exponent ?, can be expressed at criticality as integrals involving the critical eigenvector. The numerical evaluation of the corresponding analytic expressions is discussed. The method is illustrated in the context of the de Almeida-Thouless line for a spin glass on a Bethe lattice but can be generalized straightforwardly to more complex situations. © 2014 IOP Publishing Ltd and SISSA Medialab srl.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.