Mean filed study of disordered spin-$1\over 2$ antiferromagnetic systems

We present a mean filed theory picture of disordered spin-$1\over 2$ antiferromagnetic system as a function of the degree of disorder, in connection to the insulating doped semiconductors. The system is a resonant valence bond (RVB) liquid state at zero disorder, and a possible RVB glass state when the disorder is finite but weak. For a highly disordered system, we show that the essential physics is the formation and decimation of strongly coupled bonds, and the thermodynamics shows an effective power-law singularity, in qualitative agreement with renormalization group result of Bhatt and Lee.