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 $T<{T}_{c}$ . 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 ${T}_{c}$ . The time autocorrelation function within model $A$ dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power law in the Griffiths phase.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 $T<{T}_{c}$. 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 ${T}_{c}$. The time autocorrelation function within model $A$ dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power law in the Griffiths phase.

arXiv:1109.4172Physical Review BNov 14, 20119 citations

On dynamic scaling in the Heisenberg ferromagnet

Sergei V. Maleev

Physics Letters ADec 1, 19710 citations

T<{T}_{c}

. 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

{T}_{c}

. The time autocorrelation function within model

A

dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power law in the Griffiths phase.