Spectral Gap Estimates for Mixed $p$-Spin Models at High Temperature

We consider general mixed $p$-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based on an iteration scheme relating the spectral gap of the $N$-spin system to that of suitably conditioned subsystems.