New Approach to the Theory of Spin-Glasses : Principle of Minimum Free Energy and Internal Field Parameter

概要

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The Ising lattice with random distribution of binary exchange couplings {J_<ij>} is investigated. By making use of the symmetry-breaking potential method, the free energy F is first obtained for a frozen distribution of {J_<ij>}. This free energy depends on the order parameters q and m respectively for the spin-glass and ferromagnetic phases and also on a new parameter θ introduced to describe the arithmetic mean of the internal field on each spin due to the surrounding spins. A generating function is defined to calculate the averages of F, g, and m over various configurations of the exchange couplings. The phase diagram and temperature dependences of the order parameters are given explicitly for a typical case. The susceptibility has a singularity like asymmetric cusp at the transition temperature T_g, below which the spin-glass phase appears. It is found that the non-linear susceptibility diverges to negative infinity at T_g. It is to be noted that these results are obtained on the basis of the principle of minimum free energy, by taking into account the field dependency of the new parameter θ.
理論物理学刊行会の論文
1981-01-25