We study the ferromagnetic phase transition in a randomly layered Heisenberg magnet using large-scale Monte Carlo simulations. Our results provide numerical evidence for the infinite-randomness scenario recently predicted within a strong-disorder renormalization-group approach. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility, which is characterized by a nonuniversal power-law divergence in the Griffiths phase. We also study the perpendicular and parallel spin-wave stiffnesses in the Griffiths phase. In agreement with the theoretical predictions, the parallel stiffness is nonzero for all temperatures T < Tc. In contrast, the perpendicular stiffness remains zero in part of the ordered phase, giving rise to anomalous elasticity. In addition, we calculate the in-plane correlation length, which diverges already inside the disordered phase at a temperature significantly higher than Tc. The time autocorrelation function within model A dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power law in the Griffiths phase.
F. Hrahsheh et al., "Infinite-Randomness Criticality in a Randomly Layered Heisenberg Magnet," Physical review B: Condensed matter and materials physics, vol. 84, no. 18, American Physical Society (APS), Nov 2011.
The definitive version is available at https://doi.org/10.1103/PhysRevB.84.184202
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01 Nov 2011