Diluted antiferromagnets in a magnetic field: A fractal-domain state with spin-glass behavior

The phase diagram of diluted Ising antiferromagnets in the limit of a high external magnetic field B and strong dilution is investigated by a Monte Carlo simulation. The two relevant lines in the B-T plane of the phase diagram, ${\mathit{B}}_{\mathrm{eq}}$(T) which marks the onset of hysteretic effects and ${\mathit{B}}_{\mathit{c}}$(T) above which antiferromagnetic long-range order is no longer stable are determined. Between these two lines there is a broad range of high fields and low temperatures with the characteristics of a frozen-domain state. The irreversibilities observed in this state and the scaling behavior of ${\mathit{B}}_{\mathrm{eq}}$(T) both give evidence for the occurrence of a spin-glass phase. A further investigation of the relevant scaling laws for the domains leads to the conclusion that the domain state consists of fractal domains becoming stable for high magnetic fields.