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Spin and thermal conductivity in classical disordered spin chain

Transport quantities of the classical spin chain with the quenched disorder in the antiferromagnetic coupling $J_i$ are evaluated using the dynamical simulation at finite temperatures $T>0$ . Since the classical model is nonintegrable, spin and thermal conductivities remain finite even in the pure case. On the other hand, the role of disorder becomes crucial at low $T $ leading to a vanishing transport due to the Anderson localization within the linearized regime. The crossover from the insulator to the conductor appears both for the spin and thermal transport at quite low $T^* \ll J$. Still the many-body localization regime at $T>0$ evidenced by extremely short mean free paths can be strongly enhanced by introducing into the model an additional staggered field.