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.     

Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: a replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.     

Extended scaling in the magnetic critical phenomenology of the σ-phase Fe0.53-Cr0.47 and Fe0.52-V0.48 alloys

The magnetization of the sigma-phase Fe(0.53)Cr(0.47) and Fe(0.52)V(0.48) alloys was studied as a function of temperature and field. The experiments show that both materials behave magnetically as re-entrant spin glass systems. Field versus temperature diagrams were obtained where the locations of the paramagnetic phase, the intermediate ferromagnetic-like phase and the spin glass fundamental state were displayed. These diagrams are in qualitative agreement with the predictions of the mean field theory for the interplay between the ferromagnetic and spin glass orderings. The critical phenomenology near the para-ferromagnetic transition could be investigated. It was found that the paramagnetic susceptibility is quite well described by the extended scaling scheme, where the reduced temperature is written as τ = (T - T(c))/T. The value obtained for the susceptibility critical exponent γ is intermediate between the prediction of the 3D Heisenberg universality class and the large values observed in spin glasses, as previously found in other re-entrant systems. The data do not confirm the validity of the extended scaling in the ferromagnetic-like phase. Using either the conventional or extended scaling protocols, the exponents β and δ were found to have values close to those reported for spin glass transitions. Despite the relevance of disorder and the anomalous values determined for β, γ and δ, the Widom scaling relation holds as an equality.     

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.     

Competition between glassiness and order in a multispin glass

A mean-field multispin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet, and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

On the behavior of static susceptibilities in spin glasses

Linear and nonlinear susceptibilities of spin glasses in thermal equilibrium are qualitatively discussed in terms of magnetic short-range order. The apparent discrepancy between theoretical results, implying lack of Edwards-Anderson order and hence a divergence of the susceptibility at zero temperature, and experiments showing a susceptibility saturating at finite values, is considered. It is suggested that the susceptibility must indeed have a static maximum if the system exhibits a (frustrated) ferromagnetic phase with a reentrant phase boundary. At the reentrancy point, some exponents of the ferromagnet take twice their normal value, and hence a crossover near this point occurs similar to multicritical points. These observations are used to interpret a number of recent experiments, and it is shown that neither of them proves the existence of a static spin glass phase. As a quantitative example of gradual onset of order without a phase transition in three-dimensional systems, numerical results for susceptibility and specific heat of the fully frustrated Ising fcc antiferromagnet at its critical field are given.Finally the possible coexistence of spin-glass behavior and ferromagnetic long-range order in vector spin glasses with short-range interactions is discussed. Speculative arguments suggest that even for time-scales for which the spins are frozen such a coexistence should not occur, if interactions off-diagonal in the spin components (such as of dipolar origin) are included.     

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.     

Code Optimization,Frozen Glassy Phase and Improved Decoding Algorithms for Low-Density Parity-Check Codes

The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check(bit) nodes have higher decoding thresholds compared to regular counterparts with homogeneous degree distribution. We also show that the instability of the mean-field calculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed(searching for the ground state), we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is close to the dynamical transition where all local search heuristics fail to identify the true message(codeword or the ferromagnetic state). After the dynamical transition, the number of metastable states with larger energy density(than the ferromagnetic state)becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentially numerous codewords sharing the identical ferromagnetic energy.     

Viscous behavior in a quasi-1D fractal cluster glass

The spin glass transition of a quasi-1D organic-based magnet ([MnTPP][TCNE]) is explored using both ac and dc measurements. A scaling analysis of the ac susceptibility shows a spin glass transition near 4 K, with a viscous decay of the thermoremanent magnetization recorded above 4 K. We propose an extension to a fractal cluster model of spin glasses that determines the dimension of the spin clusters (D) ranging from approximately 0.8 to over 1.5 as the glass transition is approached. Long-range dipolar interactions are suggested as the origin of this low value for the apparent lower critical dimension.     

Magnetic and electrical properties of the ZnGeAs<Subscript>2</Subscript>: Mn chalcopyrite

Doping of the ZnGeAs₂ semiconductor with manganese has produced compositions with spontaneous magnetization and high Curie temperatures of up to 367 K for the composition 3.5 wt% Mn. Their magnetic properties are characteristic of spin glasses at temperatures T < T _S and magnetic fields H < 11 kOe. In stronger fields, the spin glass state transforms into a phase with a spontaneous magnetization 4–5 times weaker than that to be expected under ferromagnetic ordering of all Mn ions. This is obviously a singly-connected ferromagnetic phase containing regions with frustrated bonds. The frustrated regions and the spin glass phase have inclusions of noninteracting ferromagnetic clusters, because these regions and the spin glass phase at low temperatures exhibit a strong increase in the magnetization M, with the dependence M(T) being described by the Langevin function. Measurements of the electrical resistivity ρ and the Hall effect have revealed that, for T < 30 K, the resistivity ρ of compositions with 1.5 and 3.5 wt % Mn is higher that at 30 K, which makes superexchange dominant and gives rise to the onset of the spin glass state. The nonuniform distribution of Mn ions in the spin glass phase accounts for the existence of isolated ferromagnetic clusters, their ferromagnetism being generated by carrier-mediated exchange. As the temperature increases still more, the increase in the mobility occurs faster than the decrease in the concentration, thus promoting an enhancement of the carrier-mediated exchange and growth of the ferromagnetic clusters in size, which at T = T _S come in contact. This signifies a transition from a multiply-to a singly-connected ferromagnetic phase, which contains microregions with frustrated bonds.     

Disordered magnets

The physics of strongly-disordered magnets and especially that of spin glass is an example of a scientific problem whose ideas and results are widely used in different and sometimes rather distant areas (up to biology, for example). This is the consequence of the paradoxical nature of the main question of this problem: how does ordering occur in systems which do not possess any apparent order at all? In other words, how can one find genuine (but hidden) internal variables which determine dynamics (and thermodynamics) of the system having no macroscopic order parameter. From the theoretical point of view the “generic model” for such a system is the well-studied model of spin glass with infinite-range interaction. The next necessary step is to understand the degree of applicability of the results of infinite-range models to real systems. Further there are a number of phenomena which are completely beyond the frame of this model and are governed by fluctuation effects. The theory of fluctuation phenomena in strongly disordered magnets is at the very beginning of its development. In this report we discuss some relevant problems which have been well studied. In the case of genuine spin glasses the problems are as follows: whether there exists a thermodynamic phase transition to the spin glass phase and how does it occur? What is the physics of non-exponential relaxation far above the transition point? Further there are a number of systems belonging to the spin glass universality class (in the sense of phase-transition theory) but possessing the same sort of short-range order. We consider the following spin glasses with local helical order (for example, the diluted yttriumbased alloys YEr, YDy); amorphous magnets with strong random-axis anisotropy; disordered magnets with strong dipolar interaction. We discuss mainly the structures of low-temperature phases in these systems.     

Transverse magnetic ordering

There is an increasing number of ferromagnets and antiferromagnets which are observed to undergo either a further long range magnetic order or spin glass transition in components of the moment transverse to either the ferromagnetic or antiferromagnetic ordering direction. Necessary conditions include exchange frustration and some atomic disorder. We discuss the observation of transverse antiferromagnetic order in the ferromagnet (Fe, Mn)₃Si and the transverse spin glass phase observed in the ferromagnetic glassy metal a-(Fe, Zr) and the antiferromagnet γ-Mn–Cu.     

AC susceptibility enhancement studies in magnetic systems

Enhancement of AC susceptibility has been observed for typical ferromagnets (Gd), reentrant spin glasses like (Fe_1.5Mn_1.5Si) and canted spin systems (Ce(Fe_0.96Al_0.04)₂). The data have been interpreted with the help of a simulation model based on dry friction-like pinning of domain walls for systems having ferromagnetic domain structures. A strong pinning mechanism appears in the reentrant spin glass like and canted spin systems at low temperatures in addition to the intrinsic one in the ferromagnetic phase. The temperature variation of the pinning potential has been given qualitatively for the reentrant spin glass like systems.     

Some recent developments in spin glasses

I give some experimental and theoretical background to spin glasses, and then discuss the nature of the phase transition in spin glasses withvector spins. Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. A finite-size scaling analysis of the correlation length of the spins and chiralities shows that there is a single, finite-temperature transition at which both spins and chiralities order.     

Enhanced decoherence in the vicinity of a phase transition

We study the decoherence of a spin-1/2 induced by an environment which is on the verge of a continuous phase transition. We consider spin environments described by the ferromagnetic and antiferromagnetic Heisenberg models on a square lattice. As is well known, these two-dimensional systems undergo a continuous phase transition at zero temperature, where the spins order spontaneously. For weak coupling of the central spin to these baths, we find that as one approaches the transition temperature, critical fluctuations make the central spin decohere faster. Furthermore, the decoherence is maximal at zero temperature as signaled by the divergence of the Markovian decoherence rate.     

Spin and charge ordering in three-leg ladders in oxyborates

We study the spin ordering within the three-leg ladders present in the oxyborate Fe3O2BO3 consisting of localized classical spins interacting with conduction electrons (one electron per rung). We also consider the competition with antiferromagnetic superexchange interactions to determine the magnetic phase diagram. Besides a ferromagnetic phase we find (i) a phase with ferromagnetic rungs ordered antiferromagnetically and (ii) a zigzag canted spin ordering along the legs. We also determine the induced charge ordering within the different phases and the interplay with lattice instability. Our model is discussed in connection with the lattice dimerization transition observed in this system, emphasizing the role of the magnetic structure.     

Study of the kinetics of domain structures in thin ferromagnetic films by the Wang-Landau method

The features of a phase transition between the strict striped domain structure in thin ferromagnetic films with transverse anisotropy and the so-called tetragonal phase, where domains can be twisted and broken into parts, have been analyzed. It has been shown that the phase transition should be thermodynamically treated as a Kosterlitz-Thouless transition, where ends of domains serve as vortices. It has been demonstrated with the Wang-Landau numerical algorithm that the kinetics of this phase transition is strongly slowed down owing to the existence of a large number of metastable states; in this property, the system is partially similar to spin glasses.     

Aging in the ferromagnetic phase of terbium

We report on aging, rejuvenation and memory effects in the ferromagnetic phase of pure terbium. We have applied an experimental method specifically for investigating slow dynamics of spin glasses, because these effects cannot be interpreted as conventional diffusion after-effects. Results show that relaxation times of the magnetic response are widely distributed, and isothermal aging shifted the distribution towards longer durations. If the sample was heated/cooled after such isothermal aging, the relaxation times shortened as if aging was starting anew; the behavior resembles that in spin glasses. Uniform magnetization experiments indicate that, unlike rejuvenation in spin glasses, ferromagnetic correlations are not returned to disorder by thermal perturbations. In contrast with memory effects in spin glasses, the effects of isothermal aging cannot be recovered once these disappear, even if the system is returned to its initial temperature. The observed results can be explained as collective pinning of the domain walls for which the potential is given by a rugged temperature-sensitive energy landscape.     

自旋玻璃LaFeyNi5-y的磁性研究

本文报道了金属间化合物LaFe_yNi_5-y(0.5≤y≤1.1)的自旋玻璃特性。测定了样品的自旋玻璃冻结温度T_f。y≤0.9时,在一定温度下,样品中发生顺磁-自旋玻璃转变,T_f近似为y的线性函数,y≥1.0时,材料将发生顺磁-铁磁-自旋玻璃转变。 关键词：