Phenomenological Theory of Spin-Glasses and Some Rigorous Results
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A general phenomenological theory of spin-glasses is presented, which predicts the weak singularities (like cusps) of susceptibilities and specific heat near the transition point T_<SG> and also predicts generally the divergence of the second derivative of the nonlinear susceptibility with respect to a magnetic field in zero field at T_<SG>. A similar second derivative of specific heat is also shown to diverge at T_<SG> except for the molecular field theory. Scaling equations of state for magnetization m and spin-glass order-parameter q are derived, which yield new scaling relations of critical exponents for m(T), q(T), χ_0(T), C_0(T) and the corresponding nonlinear quantities. These general results explain qualitatively very well the magnetic field dependence of magnetization and specific heat observed experimentally. A non-uniform phenomenological Hamiltonian is also proposed for the renormalization group approach, which yields the critical dimensionality d_c=6, as usual. Intermediate random statistics and real replica method are proposed. There is also presented an exactly soluble model showing a spin-glass like phase transition.
- 理論物理学刊行会の論文
- 1977-10-25
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