Critical Lines in Systems with Random Anisotropy Axes

概要

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We investigate a model with random anisotropy axes and with random and non-random exchange in mean-field theory. The free energy of this model can be calculated exactly by means of replicas. Here, we consider only replica symmetric solutions. For zero anisotropy and a symmetric Gaussian distribution of exchange, the model agrees with the Sherrington-Kirkpatrick (SK) model for vector spin glasses. Additional infinite anisotropy leads in zero field to the solution of SK for Ising spins and for small fields to an instability line similar to the de Almeida-Thouless line. The free energy of a model with non-random exchange and any local anisotropy can be calculated without invoking replicas. In this case, the only order parameters are the components of the magnetization M. For random and additional cubic anisotropy and for finite magnetic fields, the high-temperature phase becomes unstable along a critical line H_c(T). This line has the same field-temperature dependence in low fields as the de Almeida-Thouless line in spin glasses. For high fields, the line H_c(T) depends on the distribution of the anisotropy axes. The properties of this line will be discussed in detail in the limits of small and infinite anisotropy.
理論物理学刊行会の論文
1987-01-20