The spin 1/2 triangular antiferromagnet with random exchange interaction is investigated using the finite size calculation. It is shown that the susceptibility diverges with a small randomness as T→0, where T is the temperature. The enhancement of the susceptibility by the randomness at low temperatures becomes larger when the Ising-like anisotropy of the exchange interaction increases. The possible connection of the divergent susceptibility to the spin glass-like order in the ground state is also pointed out.
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