Simple relation between frustration and transition points in diluted spin glasses

We investigate a possible relation between frustration and phase-transition points in two-dimensional spin glasses at zero temperature. The relation consists of a condition on the average number of frustrated plaquettes and was reported to provide very good predictions for the critical points at zero temperature, for several two-dimensional lattices. Although there has been no proof of the relation, the good correspondence in several lattices suggests the validity of the relation and an important role of frustration in the phase transitions. To examine the relation further, we present a natural extension of the relation to diluted lattices and verify its effectiveness for bond-diluted square lattices. We then confirm that the resulting points are in good agreement with the phase-transition points in a wide range of dilution rate. Our result supports the suggestion from R. Miyazaki [J. Phys. Soc. Jpn. 82, 094001 (2013), 10.7566/JPSJ.82.094001] for nondiluted lattices on the importance of frustration to the phase transition of two-dimensional spin glasses at zero temperature.