We construct and solve numerically the thermodynamic Bethe-ansatz equations for the spin-anisotropic two-channel Kondo model in arbitrary external field h. At high temperatures the specific heat and the susceptibility show power-law dependence. For h-->0 and at temperatures below the Kondo temperature T-K a two-channel Kondo effect develops characterized by a Wilson ratio 8/3, and a logarithmic divergence of the susceptibility and the linear specific-heat coefficient. A finite magnetic field, h>0, drives the system to a Fermi-liquid fixed point with an unusual Wilson ratio which depends sensitively on h.
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