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In quantum spin systems obeying hyperscaling, the probability distribution ofthe total magnetization takes on a universal scaling form at criticality. Weobtain this scaling function exactly for the ground state and first excitedstate of the critical quantum Ising spin chain. This is achieved through aremarkable relation to the partition function of the anisotropic Kondo problem,which can be computed by exploiting the integrability of the system.

Order parameter statistics in the critical quantum Ising chain