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Quenched randomness strongly affects properties of magnetic materials.Two-dimensional (2D) random singlet (RS) states emerge in random $J$-$Q$ modelby destroying valence bond solid order with spatial randomness. We examine the2D RS state in magnetic field with quantum Monte Carlo simulations. Themagnetization and susceptibilities show power-law scaling with magnetic fieldat low temperature. Moreover, they show one-parameter scaling behavior with$B/T$, and the scaling functions are remarkably consistent with aphenomenological model of random spin pairs with a singular distribution ofinteractions. These universal scaling functions can be used to diagnose 2D RSstates in experiments.

Scaling analysis of two-dimensional random singlet state in magnetic field