The Ising Model with a Transverse Field

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Abstract
The Ising model with a transverse field has been investigated for both positive and negative exchange interactions. Effective Hamiltonians are used for a pair of nearest-neighbour spins. The transition temperature and susceptibility above the transition temperature are calculated. The critical magnitude of the transverse field for which the transition temperature becomes 0 K is also evaluated. When the transverse field is absent, the result of the present method is reduced to that of the Bethe approximation.