Ground state of a spin-phonon system. III. Small-B limit

The ground state of the spin-one-half acoustic phonon system is studied in the limitB1. The technique is to combine the Brillouin-Wigner variational perturbation theory with a source canonical transformation. With theB=0 source transform the energy is calculated as a function of coupling constant through terms of orderB ². To this order there is no phase transition. The theory gives the crossover from perturbation theory to an improved classical theory with quantum fluctuations. With a source transform with a nonzero inverse length the energy estimate is further improved to next order in the coupling constant and for larger values ofB. The soft, infinite-order transition of the modified source theory is removed in the limitB1.     

Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Ground state of a spin-phonon system. II. Adiabatic limit

The phase transition for a spin in a magnetic fieldB coupled to acoustic phonons by a coupling constant is studied. The caseB1 with an upper cutoff of unity for the phonons is studied systematically by using an adiabatic canonical transformation. In leading order the transition line is at =2/B=1. In the normal phase (<1) the ground-state energy is –B/2 plus a function of that is given explicitly as the solution of a pair theory. In the broken symmetry phase (>1) the energy is the classical energy plus the same function of =1/². It is found that the first derivatives of the energy with respect to and with respect toB have finite jumps across the transition line. Quantum fluctuations in both phases are treated. Higher-order terms are a series of powers of 1/B times functions of . The case of a small transverse fieldB is also studied. The sharp transition disappears and is replaced by rapid variation in a region of order (B₁/B)^2/3 about =1.     

No room temperature ferromagnetism in Mn over-doped Zn1−xMnxO (x>0.02)

Mn-doped ZnO samples having composition Zn_1−xMn_xO (x=0.02, 0.04 and 0.05) were synthesized by solid state reaction technique with varying concentration of Mn from 0.02 to 0.05. Evidence of room temperature ferromagnetism was observed only in the composition Zn_0.98Mn_0.02O sintered at 500 °C. Our XRD pattern confirms the presence of Mn₃O₄ impurity phase in all the Zn_1−xMn_xO samples with the exception of Zn_0.98Mn_0.02O. We emphasize that the appearance of Mn₃O₄ phase in the system forbids the exchange type of interaction between the Mn ions and suppresses the ferromagnetism in all the Mn over-doped Zn_1−xMn_xO (x>0.02) system. SEM microstructure study also supports the interruption of exchange type of interaction inside the system with the increase in Mn concentration in the sample. Interestingly, for this particular composition, Zn_0.98Mn_0.02O sintered at 500 °C, glassy ferromagnetism type of transition is observed at low temperature. This type of transition is attributed to the formation of the oxides of Mn clusters at low temperature.     

Zero temperature magnetization of a one-dimensional spin glass

We calculate the zero temperature magnetizationm of a one-dimensional Ising spin glass is a weak magnetic fieldh. We show thatmCh _x and give closed expressions for the constantC and the exponentx which both depend on the probability distribution of nearest-neighbor interactions.     

Quantum Hall ferromagnetism in a two-valley strained Si quantum well

Tilted field magnetotransport study was performed in a two-valley strained Si quantum well and hysteretic diagonal resistance spikes were observed near the coincidence angles. The spike around filling factor ν=3 develops into a giant feature when it moves to the high-field edge of the quantum Hall (QH) state and quenches for higher tilt angles. When the spike is most prominent, its peak resistance is temperature independent from T20 mK up to 0.3 K, which is different from the critical behavior previously reported near the Curie temperature of the QH ferromagnet in AlAs quantum wells. Our data suggest a strong interplay between spins and valleys near the coincidence.     

The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm

We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two- and three-dimensional lattices. By a systematic analysis we find a simple formula to estimate the values of the parameters needed in the algorithm to find the GS with a fixed average probability. We also study the performance of the algorithm for single samples, quantifying the difference between samples where the GS is hard, or easy, to find. The GS energies we obtain are in good agreement with the values found in the literature. Our results show that the performance of the parallel tempering technique is comparable to more powerful heuristics developed to find the ground state of Ising spin glass systems.     

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.     

一维铁磁/有机系统的基态与自旋分布研究

文中用一维紧束缚模型描述铁磁金属,用一维非简并的Su-Schrieffer -Heeger (SSH)模型描述共轭聚合物,研究了在一维铁磁/共轭聚合物系统和一维CMR材料/ 聚合物系统中的电子转移和自旋转移.发现在聚合物部分没有自旋的双极化子比有自旋的极化子具有较低的能量而容易产生.然而在铁磁CMR材料/聚合物系统中极化子的产生能低于聚合物中极化子的产生能,增加了有机物中自旋极化输运的可能性.     

Strange attractor in the Potts spin glass on hierarchical lattices

The spin-glass q-state Potts model on d  -dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension _dl(q)$d_l(q)$ for q>2$q>2$, the coupling constants probability distribution flows to a low-temperature strange attractor   or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature _Tc(q,d)$T_c(q,d)$. The strange attractor was investigated considering four initial different distributions for q=3$q=3$ and d=5$d=5$ presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.     

Spin-dependent resistivity and quantum Hall ferromagnetism in two-dimensional electrons confined to AlAs quantum wells

We observe a strong dependence of the amplitude and field position of longitudinal resistivity (ρ_xx) peaks in the spin-resolved integer quantum Hall regime on the spin orientation of the Landau level (LL) in which the Fermi energy resides. The amplitude of a given peak is maximal when the partially filled LL has the same spin as the lowest LL, and amplitude changes as large as an order of magnitude are observed as the sample is tilted in field. In addition, the field position of both the ρ_xx peaks and plateau–plateau transitions in the Hall resistance shift depending on the spin orientation of the LLs. The spin dependence of the resistivity points to a new explanation for resistivity spikes, associated with first-order quantum Hall ferromagnetic transitions, that occur at the edges of quantum Hall states.     

A Blume-Capel spin glass with competing crystal-field interactions on a hierarchical lattice

Renormalization-group methods are used with a hierarchical lattice to model a Blume-Capel spin glass with annealed vacancies and competing crystal-field interactions. The strength of competing cross-link interactions is progressively increased as the effects, upon the phase diagrams, are investigated. A series of phase diagrams have been produced, sinks interpreted, and critical exponents calculated for higher order transitions.     

The flavour liquid state and Hund‘s rule effects in spin systems with orbital degeneracy

In order to understand the properties of the spin system with orbital degeneracy, we first generalize the linearized semiclassical spin wave method for the SU(2) generators into the SU(4) case, and then investigate the elementary excitations of the orbital-spin systems in the SU(4) limit. The results show that, due to the reduction of the dimensionality of the excitations, the ordered state of the SU(4) spin-orbital model is unstable. Secondly, we study the effects of the Hund interaction on the flavour liquid state of the system. Our mean-field results suggest that, for a small Hund interaction, the flavour liquid state is still stable against the generalized spin-density wave state, but with sufficient deviation from the SU(4) limit, the long-range order may be attained in two-dimensional systems. Finally, the implications for the experimental observations on the material LiNiO₂ are discussed.     

The spin glass correlation length and the crossover from three to two dimensions

The identification of a time and temperature dependent spin glass correlation length, ξ(t,T), has consequences for samples of finite size. Previous experiments on layered samples show a suppression of the freezing temperature with decreasing sample thickness. The correlation length exceeding the finite sample thickness can explain these results. This novel analysis lends further credence to the correlation length paradigm of understanding spin glasses.     

Acceleration of adiabatic quantum state transfer in a spin chain under zero-energy-change pulse control

We present a protocol for accelerating adiabatic quantum state transfer through a spin chain by adding an effective control pulse. Using Feshbach P-Q partitioning technique, we obtain the one-component dynamical equation which guides us to set the amplitude and period of the control field. This field can be a sequence of alternatively negative and positive (zero-energy change) pulses which can be realized easily in experiment. As an example, we discuss a three particles spin chain and the numerical calculation shows that the accelerated quantum state transfer can be obtained.     

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis

We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.     

Finite-dimensional spin glass and quantum error correcting code

We study a variety of spin systems with randomness in order to investigate the performance of the quantum error correcting codes. We show that the duality formalism is useful to search the locations of the critical points for the random spin systems, which gives us the clue to the exact values of the accuracy thresholds for the topological error correcting codes.     

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. II. Magnetized spin-glass phase and the de Almeida-Thouless line

In this and the companion paper, we analyze the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize magnetized spin-glass (MSG) phases by divergence of an appropriate susceptibility: at zero field this signals the existence of an intermediate MSG phase; at nonzero field, this is used to identify the de Almeida-Thouless line.