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arXiv:1109.4172 · Physical Review B

Infinite-randomness criticality in a randomly layered Heisenberg magnet

Fawaz Y. Hrahsheh, Hatem Barghathi, Thomas Vojta

Published Nov 14, 2011• 9 citations
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Abstract

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.

DOI
10.1103/physrevb.84.184202

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We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the critical point has exotic infinite-randomness character. It is accompanied by strong power-law Griffiths singularities. We compute various thermodynamic observables paying particular attention to finite-size effects relevant for an experimental verification of our theory. We also study the critical dynamics within a Langevin equation approach and find it extremely slow. At the critical point, the autocorrelation function decays only logarithmically with time while it follows a nonuniversal power law in the Griffiths phase.
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We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one dimension. At the critical point the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single continuously varying exponent, ${z}^{\ensuremath{'}}$, which diverges at the critical point, as in one dimension. Consequently, the zero temperature susceptibility diverges for a range of parameters about the transition.
The random field and random anisotropy N -vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg ( N =3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈 m ( r 1 ) m ( r 2 )〉∼¦ r 1 − r 2 ¦ − 0.62ε . The magnetic susceptibility diverges at low fields as χ∼ H −1+0.15ε . In the random field N -vector model the correlation length is finite at arbitrarily weak disorder for any N >3.