Correlation function and transition temperature bounds for bond-disordered Ising systems

Abstract

For spin ¹/₂ Ising models with ferromagnetic pair interactions J_ij which are taken to be statistically independent, non-negative, random variables, the authors show that the averaged two-spin correlation function ( sigma _p sigma _q) is less than or equal to the value ( sigma _p sigma _q)_J for the corresponding non-random system in which each J_ij is replaced by its average value J_ij. The inequality implies for sufficiently high temperatures that the averaged isothermal susceptibility chi or=0 and delta ( sigma _p sigma _q)/ delta J_rs>or=0 imply that delta ²( sigma _p sigma _q)/ delta J_rs²<or=0.