Response factorization of simply connected Ising lattices with application to bethe lattice spin glasses

The thermodynamics of a classical lattice gas in Ising form, with arbitrary interaction, is set up in entropy format, with multipoint magnetizations as control parameters. It is specialized to the case of one- and two-point interactions on a simply connected lattice; both entropy and profile equations are written down explicitly. Linear response functions are expressed in Wertheim-Baxter factorization and used to derive the Jacobian of the transformation from couplings to magnetizations. An arbitrary spin-glass coupling distribution is transformed to the corresponding magnetization distribution, whose effect on thermodynamic properties is assessed. A Gaussian coupling-fluctuation expansion diverges at sufficiently large fluctuation amplitude, suggesting the possibility of a phase transition.     

Spin-glass transition in a Kondo lattice with quenched disorder

We use the Popov-Fedotov representation of spin operators to construct an effective action for a Kondo lattice model with quenched disorder at finite temperatures. We study the competition between the Kondo effect and frozen spin order in Ising-like spin glass. We present the derivation of new mean-field equations for the spin-glass order parameter and analyze the effects of screening of localized spins by conduction electrons on the spin-glass phase transition.     

Half-filled Kondo lattice on the honeycomb lattice

The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening and antiferromagnetic orders in the intermediate coupling regime. In addition, the stability of Kondo insulator requires a minimum strength of the Kondo coupling. These features are attributed to the linear density of state, which are absent in the square lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is analyzed and the corresponding antiferromagnetic spin-density-wave transition falls into the O(3) universal class. Comparatively, we also discuss the Kondo necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice. Interestingly, it is found that the topological insulating state is unstable to the usual antiferromagnetic ordered states at half-filling for the KMK model. The present work may be helpful for further study on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.     

Fast nuclear relaxation in CoPd alloys studied by nuclear orientation-fast heating

We have studied the nuclear spin-lattice relaxation of Co nuclei in the Co concentration range from 1.6 ppm to 1%, using alloys containing radioactive⁶⁰Co and a nuclear orientation-fast pulsed heating (NO-FH) method. In the ferromagnetic region, relatively fast relaxation is found, in agreement with an estimate based on NMR results. The observed concentration dependence of the relaxation rate is similar to that of FePd alloys. In the spin-glass regime, a moderate field dependence of the relaxation rates is seen, obeying a concentration-scaling law. At still lower concentrations, a transition to local-moment behavior is observed.     

Energy transfer from paramagnetic ions to a lattice through rapidly relaxing centers

Spin-lattice relaxation is analyzed in a crystal containing two types of paramagnetic centers having approximately equal resonant frequencies but markedly different spin-phonon couplings. It is assumed that for the centers having the strong spin-phonon coupling this coupling is stronger than the spin-spin coupling with other paramagnetic centers. The Green's function method is used. The spin-lattice relaxation time for the centers coupled weakly with the lattice through rapidly relaxing centers is found as a function of the difference between the splittings of their spin levels, the strength of the spin-spin coupling between these centers, the concentrations of these centers, and the strength of the spin-phonon coupling over rapidly relaxing centers.Translated from Izvestiya VUZ. Fizika, No. 3, pp. 15–20, March, 1970.In conclusion the author thanks S. A. Al'tshuler and L. K. Aminov for useful discussions of these results.     

The boundary between the spin-glass and ferromagnetic states of the bond-random Ising model in the square lattice at T = 0

The bond-random (±J) Ising model in the square lattice is considered in the square cluster approximation. The boundary between the ferromagnetic and spin-glass states at T = 0 is obtained as the transition point from the asymmetric distribution of the effective fields to the symmetric distribution. The concentration of this transition, P_FG is obtained by solving the integral equation for the distribution function of the effective fields.     

Kinetic lattice models of disorder

We study a class of stochastic Ising (or interacting particle) systems that exhibit a spatial distribution of impurities that change with time. It may model, for instance, steady nonequilibrium conditions of the kind that may be induced by diffusion in some disordered materials. Different assumptions for the degree of coupling between the spin and the impurity configurations are considered. Two interesting well-defined limits for impurities that behave autonomously are (i) the standard (i.e., quenched) bond-diluted, random-field, random-exchange, and spin-glass Ising models, and (ii) kinetic variations of these standard cases in which conflicting kinetics simulate fast and random diffusion of impurities. A generalization of the Mattis model with disorder that describes a crossover from the equilibrium case (i) to the nonequilibrium case (ii) and the microscopic structure of a generalized heat bath are explicitly worked out as specific realizations of our class of models. We sketch a simple classification of transition rates for the time evolution of the spin configuration based on the critical behavior that is exhibited by the models in case (ii). The latter are shown to have an exact solution for any lattice dimension for some special choice of rates.     

Mean-field renormalization group for the q-state clock spin-glass model

The mean-field renormalization group is used to study the phase diagrams of a d-dimensional q-state clock spin-glass model. We found, for q = 3 clock, the transition from paramagnet to spin glass is an isotropic spin-glass phase, but for q = 4 clock, the transition from paramagnet to spin glass is an anisotropic spin-glass phase. However, for q ⩾ 5 clock, the result of anisotropic spin-glass phase depends on the temperature and the distribution of random coupling. While the coordinate number approaches infinity, the critical temperature evaluated by the mean-field renormalization group method is equal to that by the replica method.     

On equivalence of spin and field pictures of lattice systems

We investigate the spin and field systems on a lattice connected by the Kac-Siegert transform. It is shown that the structures of corresponding theories are equivalent (in the sense of isomorphy of space of Gibbs states and order parameters). Using the idea of equivalence of spin and field pictures, we exhibit a class of lattice systems possessing infinitely uncountably many ground states. The systems of this type with infinite-range, slow-decaying interactions are expected to have a spin-glass phase transition.     

Triangular lattice Potts models

In this paper we study the 3-state Potts model on the triangular lattice which has two- and three-site interactions. Using a Peierls argument we obtain a rigorous bound on the transition temperature, thereby disproving a conjecture on the location of its critical point. Low-temperature series are generated and analyzed for three particular choices of the coupling constants; a phase diagram is then drawn on the basis of these considerations. Our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order, implying the existence of a multicritical point in the ferromagnetic region. Relation of the triangularq-state Potts model with other lattice-statistical problems is also discussed. In particular, an Ashkin-Teller model and the hard-hexagon lattice gas solved by Baxter emerge as special cases in appropriate limits.Supported in part by NSF grant No. DMR 78-18808.     

Coupling the methyl group in acetamide to phonons: a consistent view of tunnelling and lattice dynamics

Inelastic neutron spectra of acetamide-h5 and acetamide-h2 have been measured at different temperatures below 40K and with high energy resolution in the energy range up to 15 meV. A lattice dynamical model on the basis of atom-atom potentials and electric charges obtained from first principles calculations describes the spectra well if soft internal molecular modes are included. The model is used to reproduce the temperature dependence of the tunnelling transition of the methyl group. For this purpose the density of states is split into that of an isolated rotor in a static field and that of the phonon bath. The effects of the rotor-phonon coupling are evaluated in second order perturbation theory. The broadening of tunnelling lines comes out correctly when the atom atom potentials taken from literature are scaled down by 20%. To get the shift right the strength of the coupling to the lattice needed to be different for the A type symmetry state from that for the E type state. The coupling with the low frequency phonons appears to be very weak.     

Spin glasses on thin graphs

In a recent paper [C. Baillie, D.A. Johnston and J.-P. Kownacki, Nucl. Phys. B 432 (1994) 551] we found strong evidence from simulations that the Ising antiferromagnet on “thin” random graphs — Feynman diagrams — displayed a mean-field spin-glass transition. The intrinsic interest of considering such random graphs is that they give mean-field theory results without long-range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle-point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin-glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice or in previous replica calculations.

We then investigate numerically spin glasses with a ±J bond distribution for the Ising and Q = 3, 4, 10, 50 state Potts models, paying particular attention to the independence of the spin-glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution P(q) for all of the models. The parallels with infinite-range spin-glass models in both the analytical calculations and simulations are pointed out.     

Magnetic phase diagrams of Fe–Mn–Al alloy on the Bethe lattice

The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction(J) distribution in the Blume–Capel(BC) model. Ferromagnetic(J 0) or antiferromagnetic(J 0)bonds or dilution of the bonds(J = 0) are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic(F), antiferromagnetic(AF), paramagnetic(P), or spin-glass(SG) phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.     

Semiempirical analysis of spin-lattice relaxation in rare earth Kramers' doublets

The spin-lattice coupling constants of Kramers' doublet measured in uniaxial stress experiments, are used to calculate the spin-lattice relaxation times in the direct process range. A comparison with experimental data shows that a true spin lattice relaxation time was obtained only when T₁ was measured as a function of magnetic field at high fields. We suggest that the effect of the phonon bottleneck is important at lower fields.     

三维钻石型等级晶格上量子Heisenberg系统的临界性质

利用重整化群方法,研究了三维钻石型等级晶格上的各向异性量子Heisenberg模型,获得了系统的相图和临界性质. 结果表明:对于铁磁系统,在各向同性Heisenberg极限下,系统存在有限温度的相变,并计算了系统的序参量和临界指数; 对于反铁磁系统,在各向同性Heisenberg极限下,临界温度不等于零,在临界线上不存在重入行为.     

Mixed lattice and electronic states in high-temperature superconductors

Inelastic neutron scattering measurements are presented which show the abrupt development of new oxygen lattice vibrations near the doping-induced metal-insulator transition in La(2--x)Sr(x)CuO(4). A direct correlation is established between these lattice modes and the electronic susceptibility (as measured by photoemission) inferring that such modes mix strongly with charge fluctuations. This electron-lattice coupling can be characterized as a localized one-dimensional response of the lattice to short-ranged metallic charge fluctuations.     

Metal–insulator transition and colossal magnetoresistance: relevance of electron–lattice coupling and electronic phase separation

In this article, we review the insulator–metal transition and the colossal magnetoresistance effect in manganites. The relevance of electron–lattice coupling and the resulting Jahn–Teller polaron is elaborated. The general features of electronic phase separation, which results from disorder and strain effects, are discussed along with electron–lattice coupling effects. Although a comprehensive theory is still lacking that can account for all the intricate features of manganite physics, electronic-phase separation and electron–lattice coupling appear to capture the essence of the colossal magnetoresistance effect in manganites.     

Magnetic clusters in amorphous Fe90Sc10 alloy

In order to obtain information on the nature of spin coupling in Fe-rich alloys, we performed high-precision⁵⁷Fe Mössbauer effect and magnetizations measurements in a wide temperature range. These results show that with increasing temperature amorphous Fe₉₀Sc₁₀ alloys undergo a transition from a cluster spin-glass to superparamagnetism followed by paramagnetism.