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     

Replica symmetric spin glass field theory

A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v)$g(v)$. Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v)$g(v)$ can be derived, whereas it can be exactly computed in the mean field Sherrington–Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d?6$d?6$, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.     

Modified mean-random-field theory for spin glass—ferromagnetic systems

Spin glass—ferromagnetic systems such as AuFe alloys having both the ferromagnetic and RKKY interactions are studied on the basis of a mean-random-field approximation. We obtain the phase diagram of the systems in terms of the temperature and the magnetic impurity concentration. The results roughly explain the magnetism of AuFe type alloys.     

A heuristic theory of the spin glass phase

We study the low-temperature phase of the nearest-neighbor Ising spin glass. Our analysis of gauge-invariant ground state Peierls contours suggests the existence of infinitely many disjoint Gibbs states at low temperatures, provided the dimension,d, is sufficiently large (presumablyd> 3 or 4), while ford=2 the Gibbs state is unique for all temperatures. Ind 3 we present arguments supporting the existence of a massless phase with broken spin-flip symmetry at low temperatures.     

Two site spin correlation function in Bethe-Peierls approximation for Ising model

Two site spin correlation function for an Ising model above Curie temperature has been calculated by generalising Bethe-Peierls approximation. The results derived by a graphical method due to Englert are essentially the same as those obtained earlier by Elliott and Marshall, and Oguchi and Ono. The earlier results were obtained by a direct generalisation of the cluster method of Bethe, while our results are derived by retaining that class of diagrams, which is exact on Bethe lattice.     

Variation of RKKY interaction strength in dilute AuFe alloys

From measurements of the magnetic properties of some dilute AuFe alloys we find that V₀, the strength of the Ruderman-Kittel-Kasuya-Yosida interaction, V(r) = (V₀ cos 2k_Fr)/r³, decreases rapidly from V₀ = 11.9 × 10^-36 erg cm³ at n = 42 ppm Fe to 1.03 × 10^-36 erg cm³ at 6050 ppm Fe. We suggest that the observed decrease of V₀ is due to self-damping of the RKKY oscillations, and discuss the significance of this decrease for the interpretation of other experiments on AuFe.     

Evidence of spin glass dynamics in dilute LiHoxY1-xF4

ac susceptibility measurements are presented on the dilute, dipolar coupled, Ising magnet LiHoxY1-xF4 for a concentration x=0.045. The frequency and temperature dependences of the susceptibility show characteristic glassy relaxation. The absorption spectrum is found to broaden with decreasing temperature suggesting that the material is behaving as a spin glass and not as an exotic spin liquid as was previously observed. A dynamical scaling analysis suggests a spin glass transition temperature of 43+/-2 mK with an exponent znu=7.8+/-0.2.     

Dynamic mean field theory of the SK spin glass

The existence of a great number of low-temperature phases in the SK-model of a spin glass and their ultrametric organization appears generally accepted and has been obtained by various techniques. In all cases it can be traced back to ultrametric features in the respective ansatz used. Within dynamic mean field theory I have investigated two situations in which the validity of such an ansatz can be controlled or is not made. In both cases I find only a trivial form of ultrametricity. Especially for an adiabatically cooled SK-spin glass in a small external field a single state appears to dominate below the AT-line. The transition occurs via exchange of stability rather than bifurcation, the scenario common to most other continuous phase transition. The results presented contradict the common belief.     

Phase diagram of the disordered RKKY model in dilute magnetic semiconductors

We consider ferromagnetism in spatially randomly located magnetic moments, as in a diluted magnetic semiconductor, coupled via the carrier-mediated indirect exchange RKKY interaction. We obtain, via Monte Carlo calculations, the magnetic phase diagram as a function of the impurity moment density n(i) and the relative carrier concentration n(c)/n(i). As evidenced by the diverging correlation length and magnetic susceptibility, the boundary between ferromagnetic and nonferromagnetic phases constitutes a line of zero temperature critical points which can be viewed as a magnetic percolation transition. In the dilute limit, we find that bulk ferromagnetism vanishes for n(c)/n(i) >0.1. We also incorporate the local antiferromagnetic direct superexchange interaction between nearest neighbor impurities and examine the impact of a damping factor in the RKKY range function.     

Mean field theory of a quantum heisenberg spin glass

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit. A spin-glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.     

Bethe-Peierls approximation for the disordered Ising model

We study the Ising model for an alloy with an arbitrary number of components. We develop an approximation which reduces to that of Bethe and Peierls when the concentration of one of the components is unity. We investigate within this approximation the dependence of the various thermodynamic quantities, in particularT _c, on the composition of the alloy and the magnetic properties of its constituents. Comparison with the only exact calculation available, that of F. T. Leeet al., for a linear chain, shows extremely satisfactory agreement.Research supported by ARO (D). It has also benefited from the general support of Materials Science at the University of Chicago by the NSF.     

Spin glass dynamics in RKKY interacting disordered magnetic system

Using the dynamical Monte Carlo method we investigate the nonequilibrium effects in RKKY-coupling disordered spin glass. By the simulation we reproduce the well-known aging and memory phenomena and find the energy relaxation at a certain temperature happens only to the corresponding spins, which directly causes the nonequilibrium effects. Combining the master equation and the energy relaxation we analyse these phenomena and explain them from the dynamical perspective.     

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.     

The Sherrington-Kirkpatrick spin glass model: Results of a new theory

A new solution of the Sherrington-Kirkpatrick spin glass model is discussed which is valid below the temperature where the replica method becomes unstable. The free energy is lowered, the entropy has no unphysical properties forT 0. The specific heat approaches zero exponentially and has a second maximum near a lower critical temperature for given external field. Near the critical point the difference of the free energy to that of Sherrington and Kirkpatrick is extremely small. Thus the Sherrington-Kirkpatrick phase may be undercooled.     

Disordered RKKY lattice mean field theory for ferromagnetism in diluted magnetic semiconductors

We develop a lattice mean field theory for ferromagnetic ordering in diluted magnetic semiconductors by taking into account the spatial fluctuations associated with random disorder in the magnetic impurity locations and the finite mean free path associated with low carrier mobilities. Assuming a carrier-mediated indirect RKKY exchange interaction among the magnetic impurities, we find substantial deviation from the extensively used continuum Zener model Weiss mean field predictions. Our theory allows accurate analytic predictions for Tc and provides simple explanations for a number of observed anomalies, including the non-Brillouin function magnetization curves, the suppressed low-temperature magnetization saturation, and the dependence of Tc on conductivity.     

Kinetic perturbation theory for dilute gases

We prove, for two classes of smooth, repulsive interparticle potentials ø(r) = ø₀(r) + δø₁(r), that the collision integ rals of the linearized Boltzmann equation are analytic functions of λ in the neighborhood of λ = 0. It then follows, for example, that the first Enskog approximation for the transport coefficients can be represented by a power series in λ.     

Supersymmetric spin glass

The manifestly supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta function form the moduli space ℳ=RP ², where two types of phases are found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase, which may be interpreted as a spin glass phase. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 657–662 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Replica field theory and renormalization group for the Ising spin glass in an external magnetic field

We use the generic replica symmetric cubic field theory to study the transition of short-range Ising spin glasses in a magnetic field around the upper critical dimension. A novel fixed point is found from the application of the renormalization group. In the spin-glass limit, this fixed point governs the critical behavior of a class of systems characterized by a single cubic parameter. For this universality class, the spin-glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, however, behaves unusually. The physical consequences of this unusual behavior are discussed, and a comparison with the conventional de Almeida-Thouless scenario is presented.     

Scaling and infrared divergences in the replica field theory of the Ising spin glass

Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w². Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w² and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed. Received 23 December 1998 and Received in final form 23 March 1999