1/σ expansion for critical concentrations in the diluted spin glass

The author studies the threshold concentrations, P q , for critical behaviour at zero temperature in the correlation functions χ (2q) for an Ising spin glass in which nearest-neighbour interactions randomly assume the values +J, 0, and -J with respective probabilities p/2, 1-p and p/2. Here χ (q) ≡σ j (s i s j ) q ) av , where ( ) denotes an average over the ground states for fixed configuration of J and ( ) av an average over all such configurations. Due to frustration effects p c <p 2 <p 4 <p 6 . . .<p infinity , where p c is the percolation threshold. Thus spin-glass theory with only χ (2) critical (at p=p 2 ) applies and the critical exponents along the T=0 axis are the same as thermal critical exponents for p=1. When the values +J and -J are replaced by distributions of narrow width, the frustration is removed and percolation exponents are expected at p=p c .