Asymptotic dynamics of a frustrated model with spherical constraint

• We solve the long-time dynamics of a model with ferro and antiferromagnetic interactions and spherical restriction.
• We find the critical behavior of spatial and self-correlations.
• The new results are analyzed in the frame of existing literature on glassy states and thin films.

We solve the Langevin dynamics of a continuum model with a spherical constraint, considering a ferromagnetic exchange and a long-range antiferromagnetic interaction. Analytical results within the Hartree approximation show an equivalence in the form of spatial and auto-correlation functions in the long time regime between this model and the recently studied Ginzburg–Landau frustrated model. The low-temperature behavior is discussed in the context of glassy dynamics. The emergence of interesting features regarding the establishment of the saturated phase is also analyzed in the view of recent literature.