Spreading of damage in the Sherrington—Kirkpatrick spherical spin glass

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Abstract By considering the Langevin dynamics of the Sherrington—Kirkpatrick spin glass and with a spherical constraint, we calculate the asymptotic distance between two real replicas that evolve with the same thermal noise from different initial conditions. Despite the simplicity of the model its dynamics are known to be non-trivial and present ageing phenomena. We found that the asymptotic distance between two replicas is strongly dependent on the initial conditions and shows a dynamical transition at a temperature equal to the static phase transition temperature.