Location of the Ising Spin-Glass Multicritical Point on Nishimori\u27s Line

We present arguments, based on local gauge invariance, that the multicritical point of Ising spin-glasses should be located on a particular line of the phase diagram known as Nishimori\u27s line [tanh(βJ)=2p−1 for the ±J distribution]. One scaling axis is along the line, and the other is along the temperature direction. This scenario is generic for any random Ising model with a Nishimori line, in any number of dimensions, if the transitions are second order. The renormalization-group fixed point located inside Nishimori\u27s manifold is expected to control multicriticality for a wider class of models

ε Expansion for the Nishimori Multicritical Point of Spin Glasses

The renormalization-group recursion relations obtained by Chen and Lubensky for the multicritical point associated with simultaneous critical fluctuations in both the spin-glass and ferromagnetic order are reanalyzed. To first order in ε==6-d we find that the multicritical fixed point is located inside the Nishimori manifold and that the scaling axes agree with those obtained recently from general arguments. It is confirmed that the scaling along the Nishimori line and at the paramagnetic-spin-glass transition are related. We also point out some universal properties of the multicritical point of possible experimental interest

Planar, time-optimal, rest-to-rest slewing maneuvers of flexible spacecraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76605/1/AIAA-20370-687.pd

Randomly coupled minimal models

Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$ models, in the infra-red limit. This result is then extend to the case with $M$ randomly coupled $M_p$ models, which will flow toward $M$ decoupled $M_{p-1}$.Comment: 12 pages, latex, 1 eps figures; new results adde

Spin‐Wave Damping and Hydrodynamics in the Heisenberg Antiferromagnet

The Dyson‐Maleev formalism is used to calculate the decay rate of antiferromagnetic spin waves at low temperatures and long wavelengths. Various regimes must be distinguished depending on the relation between the wavevector k, the temperature T, and the anisotropy energy. For the isotropic system the relevant parameters are (a) the incident energy, (b) the thermal energy, (c) the deviation from linearity ( curvature energy\u27\u27) of thermal spin waves, and (d) the curvature energy of the incident spin wave. In the anisotropic case the damping of the k=0 mode has the same dependence on spin‐wave energy as in the isotropic system. In all cases, the decay rate is small compared to the frequency, which implies that the spin waves are appropriate elementary excitations for small k and T, and that they interact weakly among themselves in this limit. For k→0 with T fixed, the decay rate is proportional to k 2 in the isotropic system. This agrees with an earlier hydrodynamic prediction and contradicts previous microscopic calculations. In this low‐k limit the full spin‐spin correlation function is calculated, and it agrees with the hydrodynamic form proposed earlier. The possibility of experimental verification of these predictions is briefly discussed

Dynamics of an Antiferromagnet at Low Temperatures: Spin-Wave Damping and Hydrodynamics

The Dyson-Maleev boson formulation is used to investigate the dynamical properties of Heisenberg antiferromagnets at long wavelengths and low temperatures. Various regimes for the decay rate of spin waves are found, depending on the relation between the wave vector k, the temperature T, and the anisotropy energy ℏωA, and in all cases the decay rate is much smaller than the spin-wave frequency. This result implies that spin waves are well-defined elementary excitations, which interact weakly at low temperatures and long wavelengths, in contrast to results obtained by previous authors, but in close analogy with the ferromagnetic case. When the long-wavelength limit is taken at fixed temperature, the decay rate Γk⃗ is proportional to the square of the frequency ωEεk⃗ , where ωE is the exchange frequency. In the quantum-mechanical low-temperature limit (ST≪TN), we find Γk⃗ =2ωES−2ε2k⃗ τ3(2π)−3(a∣1nτ∣+a′) for εk⃗ ≪τ3≪1, where τ=2kBT/ℏωE, and S is the spin quantum number. In the classical low-temperature limit (TN/S≪T≪TN), we find Γk⃗ =(4η/3π)ωE(T/TN)2ε2k⃗ for εk⃗ ≪1. For small uniaxial single-ion anisotropy [ε0~(2ωA/ωE)1/2≪1], we find Γ0=3/2ωES−2ε20τ3(2π)−3(a∣1nτ∣+a\u27\u27) for ε0≪τ3≪1. (In these expressions, a, a′, η, and a\u27\u27 are all constants of order unity.) Results are also obtained for other regimes, and for the damping of a spin wave driven off resonance. In each case, the nature and self-consistency of the perturbation expansion are examined in detail. For the isotropic system, the full frequency-dependent transverse spin-correlation functions are calculated in the long-wavelength limit, and are found to agree with the forms previously obtained by hydrodynamic arguments. By a comparison of the two forms, the transport coefficients are determined at low temperatures. Several of the calculations have been performed using the Holstein-Primakoff as well as the Dyson-Maleev representations. The results for observable quantities agree in the two formalisms, except at the longest wavelengths, where the Holstein-Primakoff expressions are not self-consistent in lowest order. Finally, the possibility of experimental verification of the present calculations is briefly discussed