Replica symmetry breaking in a fermionic cluster spin glass model in a transverse field

We analyze a fermionic Ising spin glass model in the presence of a transverse magnetic field Γ within a cluster mean field theory. The model considers a Sherrington-Kirkpatrick type interaction between magnetic moments of clusters with a ferromagnetic intra-cluster coupling J₀. The spin site operators are written as a bilinear combination of fermionic operators. In these quantum spin glass model, the inter-cluster disorder is treated by using a framework of one-step replica symmetry breaking within the static approximation. The effective intra-cluster interaction is then computed by means of an exact diagonalization method. Results for several cluster size n_s, values of Γ and J₀ are presented. For instance, the specific heat shows a broad maximum (for n_s>1) at a temperature above the freezing temperature T_f, which is characterized by the inter-cluster replica symmetry breaking. Phase diagrams T versus Γ show that the critical temperature T_f(Γ) decreases for any value of n_s when Γ increases until it reaches a quantum critical point at some value of Γ_c.     

Fermionic van Hemmen spin glass model with a transverse field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field Γ. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by Γ. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential μ and Γ. The Γ field suppresses the magnetic orders. The increase of μ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by μ. In addition, μ can change the nature of the phase boundaries introducing a first order transition.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

The stability of a spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field Γ. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues λ_± of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when Γ is increased. Therefore, this result suggests that the study of the replicon cannot be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the λ_± indicate instability problems for the SG solution close to all ranges of a first order boundary.     

Critical behaviour of the ising model in a transverse field

A theory for the critical behaviour of the Ising model in a transverse field is presented. The existence of a central component in the spectral density of the longitudinal spin relaxation function is shown to result self-consistently from decay into itself and energy-fluctuation diffusion mode. Estimates of the various quantities are made forT nearT _c , the damping is seen to be temperature dependent. Our theory is appropriate for the caseΓ ～J whereΓ andJ are the magnitudes of the transverse field and the exchange interaction between the spins respectively. Its relevance to neutron scattering data on Van Vleck paramagnets is discussed.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

On the susceptibility exponent of random anisotropy magnets

The temperature dependence of the non-linear susceptibility ≈₂(T) of random anisotropy magnets in the Ising limit (speromagnets) is calculated for temperatures above the freezing temperature T_f within the framework of the correlated molecular field theory. For the effective susceptibility exponent λ_s(T) = (T?T_f)≈₂d^-1_≈2/dT a non-monotonic temperature dependence is found as for the case of spin glasses. This must be taken into account in order to obtain reliable values for the critical susceptibility exponent from experimental data.     

Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field Γ. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean J₀ and standard deviation J. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small g (g is the strength of the local superconductor coupling written in units of J), while the PAIR phase appears as unique solution for large g. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of Γ.     

Inverse freezing in the Hopfield fermionic Ising spin glass with a transverse magnetic field

The Hopfield fermionic Ising spin glass (HFISG) model in the presence of a magnetic transverse field Γ is used to study the inverse freezing transition. The mean field solution of this model allows introducing a parameter a that controls the frustration level. Particularly, in the present fermionic formalism, the chemical potential μ and the Γ provide a magnetic dilution and quantum spin flip mechanism, respectively. Within the one step replica symmetry solution and the static approximation, the results show that the reentrant transition between the spin glass and the paramagnetic phases, which is related to the inverse freezing for a certain range of μ, is gradually suppressed when the level of frustration a is decreased. Nevertheless, the quantum fluctuations caused by Γ can destroy this inverse freezing for any value of a.     

Correlated spin dynamics in 2-D quantum Heisenberg antiferromagnets from NMR relaxation in copper formiate tetradeuterate

Proton nuclear magnetic resonance (NMR) T₁ in a single crystal of copper formiate tetradeuterate is used to study the correlated Cu²⁺ spin dynamics and to derive the temperature behavior of the in-plane magnetic correlation length. The results are compared with the predictions of recent theoretical models for the spin dynamics in planar quantum Heisenberg antiferromagnets in a wide temperature range (from the Néel temperature up to a reduced temperatureT/J ～ 1.4, withJ in-plane exchange integral). In particular, it is shown that, in contrast to the predictions of the nonlinear σ model, no crossover to a quantum critical regime occurs and that the experimental findings are well reproduced by deriving the NMR relaxation rate in the framework of the standard mode-mode coupling theory.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

InAs量子点中自旋-轨道相互作用下电子自旋弛豫的参量特征

本文在处理InAs单电子量子点哈密顿模型时,将自旋-轨道(SO)相互作用作为微扰项,计算在Fock-Darwin本征函数下SO相互作用的矩阵元,利用其对能级和波函数的二阶修正,并且考虑新的能级对g因子和有效质量m^*的影响,计算得到在声子协助下电子的自旋弛豫率Γ的表达式.给出了InAs量子点中声子协助的电子自旋弛豫率Γ对于限制势频率ω₀、温度T、纵向高度z_{0关键词： 自旋弛豫率 自旋-轨道(SO)相互作用 InAs量子点 Fock-Darwin本征函数}     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

Magnetostriction and other magnetic properties of Co-Ni based amorphous alloys

The magnetostriction coefficients λ_s of (Co_1−xNi_x)₇₅Si₁₅B₁₀ amorphous alloys have been determined in the range 0 ⩽ x ⩽ 0.41. The dependence of the magnetostriction on temperature T has been related to that of the magnetic polarization J_s in a phenomenological way as λ_s(T) = α[J_s(T)]³ + β[J_s(T)]². The compositional dependence of the coefficients α and β has been obtained.From the studies of the magnetostriction in the region close to the Curie temperature it has been possible to evaluate the magnetostriction critical exponent K.     

Physics of the pseudogap phase of high Tc cuprates, or, RVB meets umklapp

It is argued that the dominant feature of the phase diagram of the high T_c cuprates is the crossover to the pseudogap phase in the energy (temperature) region E(T^∗). We argue that this scale is determined by the effective anti-ferromagnetic interaction which we calculate to be J_eff=J_{superexchange}−xt where x is the hole percentage and t the hopping integral.     

Note on the two inequivalent spin 1/2 baryon field operators

There are two inequivalent spin 1/2 local baryon field operators that can be constructed from 3 quarks. A priori theJ ^P =1/2⁺ baryons can couple to any linear combination of these operators. We show however that the coupling of the 1/2⁺ baryons to these operators is determined by the value of theSU(3) ratio ofF toD type pseudoscalar-baryon couplings. The experimental value of this ratio implies, for example, that the proton couples strongly to (u ^T C _γ d)u and weakly to (u ^T C d)γ _s u. This is of interest in QCD sum rule applications.     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

Dynamics of the infinite-range ising spin glass

The Glauber dynamics of an Ising spin glass with infinite-range interactions and additional static field, h, is investigated near the freezing temperature, T_f. We obtain critical slowing down at and below the de Almeida-Thouless instability line, h_c(T), to order (1?T/T_f)³ with algebraic decay of the spin correlations ～t^?ν, where $\text{ν=}\text{1}\text{2}$ at T_f and $\text{ν≤}\text{1}\text{2}$ for T<T_f.     

Van Vleck paramagnetism of the thulium garnet Tm3Al5O12

The magnetic susceptibility of the garnet-type single crystal Tm₃Al₅O₁₂ exhibits the typical Van Vleck temperature independent paramagnetism below ≈8 K. The temperature dependence of the susceptibility over the range 2.0-300 K has been analyzed on the assumption that the cubic crystal-electric-field dominates the energy level on ³H₆ (J=6) ground multiplet for Tm³⁺ ion having 12-electrons in 4f shell. The ground state of the ³H₆ is nonmagnetic with Γ₂ singlet, avoiding the Kramers doublet. The energy separation between Γ₂ and the first excited state Γ⁽²⁾₅ triplet is evaluated to be 68.0 K. The whole energy interval Δ between Γ₂ and the highest state Γ₁ in ³H₆ is estimated to be 339.5 K.     

Modeling of magnetic susceptibility of an antiferromagnetic system with disorder-driven quantum critical behavior

A simple model has been proposed for an antiferromagnetic system in which the quantum critical regime is induced by disorder. The proposed model makes it possible to find the magnetic susceptibility for an arbitrary ratio of the temperature T to the characteristic magnitude of the exchange integral J in a disordered magnet. The model analytically describes the crossover from the power dependence χ ～ 1/T ^ξ, which is characteristic of the ground state (the Griffiths phase, T ? J), to a dependence of the Curie-Weiss type (T ≥ J) with the effective parameters dependent on the characteristics of the distribution function of the exchange integrals. The characteristic size of spin clusters forming the Griffiths phase has been estimated. It has been demonstrated using iron-doped germanium cuprate as an example that, within the proposed approach, the experimental data can be adequately described over a wide temperature range in which the temperature changes by more than two orders of magnitude and the magnetic properties of the Griffiths phase are determined by spin clusters of nanometer size.