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It is proved that replica symmetry is not broken in the transverse andlongitudinal random field Ising model. In this model, the variance of spinoverlap of any component vanishes in any dimension almost everywhere in thecoupling constant space in the infinite volume limit. The weakFortuin-Kasteleyn-Ginibre property in this model and the Ghirlanda-Guerraidentities in artificial models in a path integral representation based on theLie-Trotter-Suzuki formula enable us to extend Chatterjee's proof for therandom field Ising model to the quantum model.

Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model