Neutron diffraction is used to investigate the field-induced, antiferromagnetically ordered state in the two-leg spin-ladder material (Hpip)2CuBr4. This classical phase, a consequence of weak interladder coupling, is nevertheless highly unconventional: its properties are influenced strongly by the spin Luttinger-liquid state of the ladder subunits. We determine directly the order parameter (transverse magnetization), the ordering temperature, the spin structure, and the critical exponents around the transition. We introduce a minimal, microscopic model for the interladder coupling and calculate the quantum fluctuation corrections to the mean-field interaction.
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