Critical properties of random anisotropy magnets

The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.     

Phase transitions in random anisotropy magnets

We report a study of magnetic properties and phase transitions in random anisotropy glasses rich in the rare-earth elements Gd, Tb and Nd. For the Gd glass, which has a small magnetic anisotropy, we find an extremely large, possibly infinite, susceptibility below 120 K and no intrinsic spontaneous magnetization. Below 55 K an hysteretic state develops. The Tb and Nd glasses, both of which have large anisotropy, exhibit transitions to a speromagneic state and they do not show an infinite susceptibility phase. The results are discussed in terms of recent theoretical predictions concerning phase transitions in the presence of random magnetic anisotropy.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

On the dynamics of Heisenberg magnets with lattice anisotropy near the phase transition

The kinetic theory (mode-mode coupling theory) is applied to lattice anisotropic Heisenberg ferromagnets and anti-ferromagnets in the paramagnetic region near the phase transition. The distinction of a hydrodynamic and a critical region is refined by introducing regimes of essentially lower-dimensional (1-d or 2-d) behavior and three-dimensional behavior of the magnet. In the regime of 3-d behavior the scaling function of the line-width of the dynamic spin correlation function is discussed extensively.     

Critical behaviour of random compressible magnets

The critical properties of a compressible random magnet are studied using renormalization group methods. Then-component orderparameter is coupled to quenched disorder and to the elastic fluctuations of the anisotropic solid. It is shown, that the critical behaviour of a compressible random magnet is in general the same as that of a random magnet on a rigid lattice. However, if the specific heat exponent of the ideal magnet is positive and the disorder is sufficiently weak, a macroscopic instability may prevent the system in reaching the critical point. The resulting first-order transition may be preceded by pseudocritical behaviour characteristic to pure compressible magnets. The effect of random magnetic fields on the critical properties of compressible magnets is also discussed.     

Note on the susceptibility exponent for two-dimensional percolation

Analyses of mean site content, mean bond content, mean perimeter and related quantities give a susceptibility diverging as (p _c –p)^–, with 2.41±0.025. This exponent disagrees with some earlier estimates but it is consistent with the (p _c –p)^–2.388... divergence predicted by the formulas of den Nijs, Nienhuis et al. and Pearson.     

Renormalization group study of random quantum magnets

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ～ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erd?s-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.     

A finite-time exponent for random Ehrenfest gas

We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit.     

Novel domain growth law in random magnets

We investigate the kinetics of domain growth in Ising magnets where a fraction 1 - p of the magnetic atoms or ions (spins) are randomly substituted by non-magnetic impurities. We argue that close to the percolation threshold p_c, the statistical self-similarity of the underlying structure gives rise to a novel crossover in the growth law. We propose a method to detect any evidence of this new prediction from the kinetics of domain growth in the dilute Ising model (DIM) during intermediate time scales by carrying out Monte Carlo simulations not at p = p_c but at slightly higher spin concentrations. We analyze the results of our extensive Monte Carlo simulation of the strongly diluted two-dimensional Ising model and find the growth to be consistent with the proposed scenario. We also compare our observations with those in the recent experiments on the kinetics of ordering in Rb₂Co_pMg_1−pF₄.     

Pair model of anisotropy and magnetostriction in soft amorphous magnets

A pair model for amorphous alloys has been developed, considering both the spherical symmetry (isotropic alloys) and the cylindrical one (alloys exhibiting pair ordering or microstructural anisotropy). The elastic energy has been first derived. Then starting from the Heisenberg exchange, the pseudodipolar (PSD), the cluster electric field (CEF) and the simple dipolar couplings, the magnetoelastic coupling and magnetic anisotropy energies have been written in the limiting case of a very small random anisotropy.     

Theta-point exponent for polymer chain in random media

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that the-point size exponent _p ⁰ of polymer chains remains unchanged for small disorder concentration (p>p _c ). At the percolation thresholdp=p _c , using a Flory-type approximation, we conjecture that _pc ⁰ =5/(d _B +7), whered _B is the percolation backbone dimension. It shows that the upper critical dimensionality for the-point transition atp=p _c shifts to a dimensiond _c >3. We also propose that the-point varies practically linearly withp for 1>pp _c .     

Note on the “susceptibility” exponent for two-dimensional percolation

Zeitschrift für Physik B Condensed Matter - New percolation series derived by Duarte and Ruskin are analysed with a recently developed method of series analysis which explicitly accounts for...     

Large quantum nonlinear dynamic susceptibility of single-molecule magnets

The nonlinear dynamical response of Mn12 single-molecule magnets is experimentally found to be very large, quite insensitive to the spin-lattice coupling constant, and displaying peaks reversed with respect to classical superparamagnets. It is shown that these features are caused by the strong field dependence of the relaxation rate due to the detuning of energy levels between which tunneling takes place. The nonlinear susceptibility technique, previously overlooked, is thus proposed as a privileged probe to ascertain the occurrence of quantum effects in mesoscopic magnetic systems.     

Quasi-long-range order in the random anisotropy Heisenberg model

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. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Effect of single ion anisotropy on the critical temperature of classical quasi-one-dimensional magnets

The effect of single ion anisotropy energy on the three-dimensional ordering temperature of a classical quasi-one-dimensional magnetic chain is estimated using a mean field approximation for the interchain coupling and a classical spin field model for a chain. Numerical results are presented for T_c as a function of the interchain and interchain exchange interactions and the single ion anisotropy.