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

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Abstract
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 Tg, below which the spin-glass phase appears. It is found that the non-linear susceptibility diverges to negative infinity at Tg. 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.

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