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The critical exponent beta =0.17(1) for the three-dimensional random-fieldIsing model (RFIM) order parameter upon zero-field cooling (ZFC) has beendetermined using extinction-free magnetic x-ray scattering techniques forFe(0.85)Zn(0.15)F2. This result is consistent with other exponents determinedfor the RFIM in that Rushbrooke scaling is satisfied. Nevertheless, there ispoor agreement with equilibrium computer simulations, and the ZFC results donot agree with field-cooling (FC) results. We present details of hysteresis inBragg scattering amplitudes and line shapes that help elucidate the effects ofthermal cycling in the RFIM, as realized in dilute antiferromagnets in anapplied field. We show that the ZFC critical-like behavior is consistent with asecond-order phase transitions, albeit quasi-stationary rather than trulyequilibrium in nature, as evident from the large thermal hysteresis observednear the transition.Comment: 12 pages, 18 figure

physical review. b, condensed matter and materials physics

Quasistationary criticality of the order parameter of the three-dimensional random-field Ising antiferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>0.85</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Zn</mml:mi><mml:mn>0.15</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">F</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>: A synchrotron x-ray scattering study

Quasistationary criticality of the order parameter of the three-dimensional random-field Ising antiferromagnetFe0.85Zn0.15F2: A synchrotron x-ray scattering study