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A phase transition of a model compound of the long-range Ising spin glass(SG) Dy$_{x}$Y$_{1-x}$Ru$_{2}$Si$_{2}$, where spins interact via the RKKYinteraction, has been investigated. The static and the dynamic scaling analysesreveal that the SG phase transition in the model magnet belongs to themean-field universality class. Moreover, the characteristic relaxation time infinite magnetic fields exhibits a critical divergent behavior as well as inzero field, indicating a stability of the SG phase in finite fields. Thepresence of the SG phase transition in field in the model magnet stronglysyggests that the replica symmetry is broken in the long-range Ising SG.

Existence of a phase transition under finite magnetic field in the long-range RKKY Ising spin glass Dy$_{x}$Y$_{1-x}$Ru$_{2}$Si$_{2}$