Dynamical scaling for spin waves in dilute ferromagnets

The ambiguity in the application of the principle of dynamic scaling to spin waves in dilute ferromagnets is resolved by taking account of the fractal nature of the infinite percolation cluster.     

Aging phenomena in spin glasses and frustrated ferromagnets

An experimental protocol developed for spin glasses has been applied to a reentrant system. We compare the main features of the aging phenomena in both spin glass and ferromagnetic phases.     

Ferromagnetic modes in spin glasses and dilute ferromagnets

We generalize the theories for the dynamics of spin glasses of Halperin and Saslow, and Dzyaloshinskii and Volovik to include additional partial ferromagnetic order. We find that the sixfold degenerate antiferromagnetic spin wave modes obtained in both theories split into two longitudinal and 2×2 transverse modes with different dispersion. In a certain range of wave vectorsq one obtains antiferromagnetic, ferromagnetic, andq-independent modes. The damping of these modes is calculated for a phenomelogical hydrodynamic model and their implications for the specific heat and electrical resistivity are discussed.     

Tapping spin glasses and ferromagnets on random graphs.

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p. This dynamics leads to a stationary regime with a steady state energy E(p). We analytically solve this dynamics for the one-dimensional ferromagnet and +/-J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.     

The magnetic phase transition in amorphous ferromagnets and in spin glasses

The magnetic phase transition in materials with exchange disorder (amorphous ferromagnets, spin glasses) is discussed. In the critical temperature range the behavior of amorphous ferromagnetic transition metal-metalloid glasses is found to be similar to the one derived for a three-dimensional homogeneous Heisenberg ferromagnet. The most prominent difference between disordered and homogeneous materials is manifested in a large temperature range of deviations from the mean field behavior beyond the critical region, as observed experimentally for the temperature dependence of the linear susceptibility of amorphous ferromagnets and of the nonlinear susceptibility of spin glasses. A molecular field theory with correlations in space and time is developed, which relates the deviations from the mean field behavior to the interplay between the temperature dependent thermal correlations in the spin system and the spatial fluctuations of the material. Application to dynamical processes (kinetic critical slowing down) is discussed.     

Activated scaling of classical and quantum spin glasses

A model for thermally activated dynamics in disordered systems shows that the linear and nonlinear susceptibility follows a generic exponential form with a "critical rounding," chi(1) proportional to chi(3) proportional to [T ln(t/tau(0)')/K](gamma/b phi) exp - [Tt(g)(phi b)ln(t/tau(0)'/K)](nu/b) (T=temperature, t=time, K=barrier constant, t(g) = 1 - T(SG)/T, and T(SG) = transition temperature; gamma>0 for chi(3) and <0 for chi(1)). This model, also valid in the presence of resonant tunneling states at energies K(0) < K [provided that K is replaced by K(0)+2T ln (1/Gamma(0)), where Gamma(0)(2) proportional, variant tunnel splitting of a spin S=1], is potentially applicable to a wide variety of systems opening the way for the study of thermally activated quantum phase transitions. The famous spin-glass system LiHo(x)Y(1-x) seems to follow this model.     

Corrections to scaling are large for droplets in two-dimensional spin glasses

The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l(theta) for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the addition of a scaling correction l(-omega) in order to accurately describe droplet energies at the length scales currently probed in numerical simulations. Using this simple modification, it is now possible to explain many results which have been found in simulations of three-dimensional Ising spin glasses with the droplet model.     

Strong universality and algebraic scaling in two-dimensional Ising spin glasses

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but nonzero temperatures and provide numerical evidence that eta approximately equal 0 and nu approximately equal 3.5 in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds, in particular, for the +/- J model, with or without dilutions, and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T = 0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.     

Aspect-ratio scaling and the stiffness exponent theta for Ising spin glasses

We introduce the technique of aspect-ratio scaling to study the scale dependence of interfacial energies in Ising spin glasses, and we show how one can use it to determine the stiffness exponent theta in a clean way, with results that are independent of the domain-wall-forcing boundary conditions imposed on the system. In space dimension d = 2 we obtain theta = -0.282(3) for a Gaussian distribution of exchange interactions.     

Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of () at =0 above the AT line to a power law behaviour ()(–i) ^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to ^1/v , where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as ^1–1/v . The average relaxation time diverges as ^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i) ^v at and below the AT line.     

Validity and limitations of scaling laws in the theory of spin glasses

Current theories for the derivation of the internal-field distribution function for statistical models of spin-glasses are briefly reviewed, with reference to the form of the distribution function and the scaling behavior of the function itself and of related observable quantities.It is shown that deviations from scaling are inherent to the statistical theory itself and do not require separate mechanisms for their explanation, and the meaning of the currently-used Lorentzian-like forms of the distribution function is clarified.     

Effective spin spin interactions in the damped ferromagnets

Simanek's theory is extended by taking into account the nuclear spin excitations due to the motion of the electronic system. Damping of the magnons is found to be an extra criteria for having a finite interaction range for the nuclear spin system. The resonance excitation of Simanek's theory is due to the neglect of the second order in the hyperfine interaction.     

Absence of ordering in a class of random spin systems,including simple models for spin glasses,and a new inequality for random ferromagnets

Absence of ordering is proved for a class of one- and two-dimensional quenched random systems including the Edwards-Anderson model for spin-glasses; a new inequality for random ferromagnets is proved using FKGP-inequalities and very recent correlation inequalities due to Sherman.     

Variational method for spin waves in disordered ferromagnets

A variational method for spin waves in a disordered ferromagnet is described and is shown to give same results as obtained by a Green function method. The results of this calculation are applied to rare earth di-aluminium alloys. The spin wave dispersion relations in these alloys as a function of concentration are predicted.     

GKS inequalities for arbitrary spin ising ferromagnets

Elementary proofs of the first and second Griffiths-Kelly-Sherman (GKS) inequalities are given for higher-spin Ising systems with a Hamiltonian containing only a quadratic form in the spin variables and integer powers of single spin variables. These proofs are obtained using Gaussian random variables. A slight generalization of previous results has been obtained in that the coefficients of the even powers of the spin variables are allowed to be negative.Work supported by NSF Grant GP-36564X.     

μ+ spin relaxation in ferromagnets

We review the recent theoretical studies of the muon spin relaxation mechanisms in metallic ferromagnets.     

Excitation of spin waves in superconducting ferromagnets

This Letter presents a theoretical analysis of propagation of spin waves in a superconducting ferromagnet. The surface impedance was calculated for the case when the magnetization is normal to the sample surface. We found the frequencies at which the impedance and the power absorption have singularities related to the spin-wave propagation, and determined the form of these singularities. With a suitable choice of parameters, there is a frequency interval in which two propagating spin waves of the same circular polarization are generated, one of them having a negative group velocity.     

Frustrated percolation,spin glasses and glasses

Summary The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT _p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT _g in the same universality class of the Ising spin glass model. AboveT _p the time-dependent autocorrelation function is characterized by a single exponential, while forT _p>T>T _g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT _g the system is in glassy state with an infinitely long relaxation time. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.