| A study is made of the following model for an insulating disorder (anti)ferromagent with both short range exchange and random long range couplings between localized spins:;The S(,i) are Ising spins. The second term has infinite range. The J(,ij) are assumed to be independent random variables distributed with zero mean. (,s) is assumed to involve all the fixed (nonrandom) exchange couplings. In applications, standard models (such as the linear model) are used for a system described by (,s) alone. The model roughly describes a system such as KMn(,c)Zn(,1-c)F(,3) in which a random dipolar field is present as a result of substitutional or positional disorder. Using the replica technique the following results are obtained. (1) In the absence of an external magnetic field there is no spontaneous (staggered) magnetization when (,s) has finite range couplings. (2) A uniform field approximation to the complete equations gives results in qualitative agreement with neutron scattering experiments in KMn(,c)Zn(,1-c)F(,3). (3) Systematically correcting the uniform field approximation gives the exact spin glass transition temperature T(,g) for the model when the corrections are second order. (4) Keeping only terms composed of entirely first and second cumulants in a diagrammatic expansion in powers of the Edwards-Anderson order parameter gives a closed theory for calculating the thermodynamic functions. This method also gives the correct behavior near the correct value T(,g).;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI). |
