Loss of long range order in the 3D random field Ising model.

Abstract

We report a synchrotron magnetic x-ray scattering study of the temperature evolution of the magnetic long range order (LRO) of ${\mathrm{Mn}}_{0.75}$${\mathrm{Zn}}_{0.25}$${\mathrm{F}}_{2}$ in a magnetic field with emphasis on the behavior after zero field cooling (ZFC). We show that with increasing temperature the metastable ZFC LRO vanishes continuously at a temperature well above the equilibrium ${\mathit{T}}_{\mathit{N}}$; the LRO follows a rounded power law with exponent ${\mathrm{\ensuremath{\beta}}}_{\mathrm{ZFC}}$=0.20\ifmmode\pm\else\textpm\fi{}0.02 and a transition width which scales as \ensuremath{\sim}${\mathit{H}}^{2}$ but with no divergent critical fluctuations. We argue that this behavior is generic to the random field Ising model.