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We study link-diluted $\pm J$ Ising spin glass models on the hierarchicallattice and on a three-dimensional lattice close to the percolation threshold.We show that previously computed zero temperature fixed points are unstablewith respect to temperature perturbations and do not belong to any criticalline in the dilution-temperature plane. We discuss implications of the presenceof such spurious unstable fixed points on the use of optimization algorithms,and we show how entropic effects should be taken into account to obtain theright physical behavior and critical points.

Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings