Scaling stiffness and correlations in the spin-glass-ferromagnet transition: evidence for the mixed phase

Results of numerical studies on the equilibrium scaling stiffness energy for 2D nearest-neighbour Heisenberg systems at T=0 are presented. The authors first consider the percolation problem and estimate the critical exponent for the spin wave stiffness to be close to 1. They then consider systems in which -J-bonds appear with probability x and +J-bonds with probability (1-x). The scaling stiffness energy, a measure of sensitivity to changes in the boundary conditions, disappears exponentially with x at x c approximately=0.13 (an estimate for large systems). This value of concentration is identified as an upper boundary of the usual ferromagnetic phase. Nevertheless the magnetisation persists above x c and disappears at X c approximately=0.30 when the system enters into the spin glass phase. The region between x c and X c is identified as corresponding to the Gabay-Toulouse mixed phase in which the system looks like a spin glass but has some non-zero magnetisation. This interpretation receives further support from studies of the two- and four-spin correlation functions in local energy minima. The correlations decay exponentially, at least on small distances. The correlation lengths of the two-spin correlations start to drop at x c . The spin components parallel to the magnetisation are actually less correlated than the transverse ones.