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

Abstract

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.

References in corpus (12)

• The Suprafroth (Superconducting Froth)
• Phase diagram of an Ising model for ultrathin magnetic films
• (Ir-)Reversibility and thermal equilibrium in magnetic domain pattern formation in ultra-thin ferromagnetic films
• Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
• Langevin simulations of a model for ultrathin magnetic films
• A Scaling Hypothesis for Modulated Systems
• Dynamics of a mean spherical model with competing interactions
• H-T phase diagram of the bi-dimensional Ising model with exchange and dipolar interactions
• Finite-size effects in the spherical model of finite thickness
• Langevin dynamics of fluctuation induced first order phase transitions: self consistent Hartree Approximation
• Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach
• Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions