Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquid s is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the di lute magnet model! the spin glass phase is reentrant inside the ferromagnet ic phase. An extension of the model is given, in which the spin glass/ferro magnet phase boundary is shown not to reenter inside the ferromagnetic phas e asymptotically close to the tricritical point whereas it has a turning po int at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increas e frustration to study the effect of dilution in a spin liquid state. This provides a "minimal" ordering by disorder from an Ising paramagnet to an Is ing spin glass.