Aging in Spherical Spin Glass Dynamics
We study Langevin dynamics for the pure spherical $p$-spin glass with $p\ge3$, with covariance $Nq^p$ and generator $\Delta_S+\beta\nabla_SH_N\cdot\nabla_S$, started from a uniform point independent of the disorder. We let the dimension tend to infinity on fixed time horizons and study the long-time behavior of the resulting hard-spherical Cugliandolo–Kurchan equations for the correlation $C$ and the response $R$. At every positive temperature, their solution has a unique stationary limit at bounded time differences, which satisfies the fluctuation–dissipation theorem (FDT), and its energy…
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