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Within the framework of the Ginzburg-Landau theory for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$-wave superconductors, we discuss the pairing-state phase transition in the absence of the Zeeman coupling between the Cooper pair orbital angular momentum and the magnetic field. We find that above a temperature ${T}_{*},$ the pairing state in a magnetic field is pure …