New Approach to the Theory of SpinGlasses Principle of Minimum Free Energy and Internal Field Parameter
Abstract
The Ising lattice with random distribution of binary exchange couplings J_{ij} is investigated. By making use of the symmetrybreaking potential method, the free energy F is first obtained for a frozen distribution of J_{ij}. This free energy depends on the order parameters g and m respectively for the spinglass 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 spinglass phase appears. It is found that the nonlinear 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.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 January 1981
 DOI:
 10.1143/PTP.65.83
 Bibcode:
 1981PThPh..65...83H