New Approach to the Theory of Spin-Glasses ---Principle of Minimum Free Energy and Internal Field Parameter---
The Ising lattice with random distribution of binary exchange couplings Jij is investigated. By making use of the symmetry-breaking potential method, the free energy F is first obtained for a frozen distribution of Jij. This free energy depends on the order parameters g 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.