Eur. Phys. J. B 14, 169-176 (2000)
https://doi.org/10.1007/s100510050117

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

¹ Centre de Recherches sur les Très Basses Températures (CRTBT)U.P.R. 5001 du CNRS, Laboratoire conventionné avec l'Université Joseph Fourier., CNRS, BP 166X, 38042 Grenoble Cedex, France
² Laboratoire de PhysiqueU.M.R. CNRS 5672, École Normale Supérieure de Lyon, 46, Allée d'Italie, 69364 Lyon Cedex 07, France

Received: 9 April 1999
Revised: 27 September 1999
Published online: 15 March 2000

Abstract

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids 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 dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase 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 Ising spin glass.