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The frustrated spherical model: an alternative to Ginzburg-Landau Hamiltonians with competing interactions

We solve analytically the Langevin dynamics of the classic spherical model considering the ferromagnetic exchange and a long-range antiferromagnetic interaction. Our results in the asymptotic regime, shows an equivalence in the functionality of the spatial and self-correlations between this model and the recently studied Ginzburg-Landau frustrated model within the Hartree approximation. A careful discussion is done about the low temperature behavior in the context of glassy dynamics. The appearance of interesting features regarding the establishment of the ferromagnetic phase is also analyzed in view of the effects of the spherical restriction. We propose a new variant of the spherical model in which the global restriction is substituted by an infinite set of restrictions over finite size regions. This modification leads to a new dynamical equation that suggests the appearance of the low temperature phase transition even in the non-frustrated case were the classic spherical model fails.