In this paper, we propose a new method, which combines the pair approximation with the discretized path-integral representation, to study the quantum transverse Ising model with random-field. Full phase diagrams are obtained for various random-field distributions. When applied random fields are trimodal (and bimodal), the critical properties including the possibility of the existence of the tricritical points and rcentrance phenomena are numerically analyzed in detail. In the limit z→∞, the extended mean-field result is recovered.
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