  We study the analytical solution of the Monte Carlo dynamics in the spherical
Sherrington-Kirkpatrick model using the technique of the generating function.
Explicit solutions for one-time observables (like the energy) and two-time
observables (like the correlation and response function) are obtained. We show
that the crucial quantity which governs the dynamics is the acceptance rate. At
zero temperature, an adiabatic approximation reveals that the relaxational
behavior of the model corresponds to that of a single harmonic oscillator with
an effective renormalized mass.

Condensed Matter