Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.     

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within the mean-field theory. The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian Hi of the Ising system numerically, and the first order-order phase transitions, the first order-disorder phase transitions, and the second-order phase transitions are discussed in details. Reentrant phenomena occur when the value of the transverse field is not zero and the reentrant diagram is given.     

Analytical and Numerical Studies of the One-Dimensional Spin Facilitated Kinetic Ising Model

The one-dimensional spin facilitated kinetic Ising model is studied analytically using the master equation and by simulations. The local state of the spins (corresponding to mobile and immobile cells) can change depending on the state of the neighbored spins, which reflects the high cooperativity inherent in glassy materials. The short-time behavior is analyzed using a Fock space representation for the master equation. The hierarchy of evolution equations for the averaged spin state and the time dependence of the spin autocorrelation function are calculated with different methods (mean-field theory, expansion in powers of the time, partial summation) and compared with numerical simulations. The long-time behavior can be obtained by mapping the one-dimensional spin facilitated kinetic Ising model onto a one-dimensional diffusion model containing birth and death processes. The resulting master equation is solved by van Kampen's size expansion, which leads to a Langevin equation with Gaussian noise. The predicted autocorrelation function and the global memory offer in the long-time limit a screened algebraic decay and a stretched exponential decay, respectively, consistent with numerical simulations.     

Analytical approximations for the hierarchically constrained kinetic Ising chain

The hierarchically constrained kinetic Ising model in one dimension is reviewed, and the results of several analytical approaches to the model are presented. Two standard approximation schemes, an effective-medium approximation and a mode-coupling approximation, are shown to fail. A new class of approximations, termed cluster approximations, is better suited for the model. It yields good results for the spin autocorrelation function, and also elucidates important general properties of the model—its connection with defect-diffusion models and the asymptotic long-time behavior of the autocorrelation function.     

A Compensation Temperature Study of Bond-Diluted Mixed Ising Ferrimagnetic Spin System with Different Transverse Fields

The magnetic properties of bond-diluted nearest-neighbor interaction mixed spin-1/2 and spin-1 Ising ferrimagnetic spin system with different transverse fields are investigated within the framework of the finite cluster approximation (FCA). Particular emphasis is given to the square lattice with coordination number 2 = 4 for which magnetizations are obtained. The interactions Jij are assumed to be independent random variable with distribution P(J_ij) = pδ(J_ij-J) + (1-p)δ(J_ij), where J < 0. If bond concentration p varies in the certain ranges, we find that the compensation temperature is obtained for the values of the different transverse fields Ω_1/2 and Ω₁ in a restricted region. We obtain the values of the critical different transverse fields and critical bond concentration in this paper.     

Effective-Field Theory for Kinetic Ising Model on Honeycomb Lattice

As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.     

Ground-state magnetic properties of the spin-2 transverse Ising model

The ground-state magnetic properties of the spin-2 transverse Ising model with a longitudinal crystal field are studied within the framework of mean-field theory (MFT) and effective-field theory (EFT), respectively. The phase diagrams and magnetization curves are examined in detail. It is found that the system exhibits a tricritical behavior in the ground-state phase diagrams. Some interesting phenomena have been found, especially the first-order phase transition from one ordered phase to the other ordered phase, which is due to the high spin. The spin correlation has important effect on the magnetic properties of the system. We also find that the ground-state phase diagrams of the spin-2 transverse Ising model are very different from those of the spin-3/2 transverse Ising model.     

Boundary States and Correlation Functions of Tricritical Ising Model from Coulomb-Gas Formalism

We consider the minimal conformaJ model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its one-point and two-point correlation functions.     

The spectral density approach to the Ising model in transverse field

The spectrum of the spin $\text{1}\text{2}$ Ising model in transverse field is investigated with the help of the spectral density method. The close agreement with the one-dimensional exact result and that of a series expansion is obtained.     

Long-time limit behavior of the solution to an atom＇s master equation

We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.     

A Compensation Temperature Induced by Transverse Fields in a Mixed Spin-1 and Spin-3/2 Ising Ferrimagnetic System

A mean-field theory is developed for a mixed Ising ferrimagnetic system consisting of spin 1 and spin 3/2 with different transverse fields. The phase diagram and the thermal behaviour of magnetizations are studied. We find that a compensation point induced by different transverse fields can be observed, although the system never exhibits any compensation point for either zero or uniform transverse fields. The anomalous behaviour of the initial longitudinal magnetic susceptibility in the vicinity of the compensation and critical temperatures is also obtained.     

Energy of Long-Lifetime Configurations in Zero-Temperature Dynamics

Using Monte Carlo method with zero-temperature dynamics, we investigate energy evolution of Ising spin configuration on a square lattice. The energies of some configurations exhibit long duration before those configurations reach the final state -- ground state or frozen stripe state. For ground-state dynamical realization, the duration occurs when the energy per spin is 4/L, where L is the lattice size. For stripe-state dynamical realization, the energy is slightly higher than 2/L when the duration appears in the last evolution stage. In addition, it is found that the average energy per spin in final state is approximately 2/3L.     

Fermionic Ising glasses in magnetic transverse field with BCS pairing interaction

We study a fermionic infinited-ranged Ising spin glass with a real space BCS interaction in the presence of an applied transverse field. The problem is formulated in the integral functional formalism where the SU(2) spins are given in terms of bilinear combinations of Grassmann fields. The problem is solved within static approximation and the replica symmetry ansatz combined with previous approaches used to study the critical behavior of the quantum Ising spin glass in a transverse field and the spin glass Heisenberg model with BCS pairing. Our results show that the transverse field has strong effect in the phase boundary of the spin glass phase and the PAIR phase in which there is a long range order corresponding to formations of pairs. The location of the tricritical point in the PAIR phase transition line is also affected.     

Exchange coupling and helical spin order in the triangular lattice antiferromagnet CuCrO2 using first principles

The magnetic and electronic properties of the geometrically frustrated triangular antiferromagnet CuCrO2 are investigated by first principles through density functional theory calculations within the generalized gradient approxi- mations （GGA）＋U scheme. The spin exchange interactions up to the third nearest neighbours in the ab plane as well as the coupling between adjacent layers are calculated to examine the magnetism and spin frustration. It is found that CuCrO2 has a natural two-dimensional characteristic of the magnetic interaction. Using Monte Carlo simulation, we obtain the Neel temperature to be 29.9 K, which accords well with the experimental value of 24 K. Based on non- collinear magnetic structure calculations, we verify that the incommensurate spiral-spin structure with （110） spiral plane is believable for the magnetic ground state, which is consistent with the experimental observations. Due to intra-layer geometric spin frustration, parallel helical-spin chains arise along the a, b, or a＋ b directions, each with a screw-rotation angle of about I20°. Our calculations of the density of states show that the spin frustration plays an important role in the change of d-p hybridization, while the spin-orbit coupling has a very limited influence on the electronic structure.     

Damage Spreading in the Ising Model with a Special Metropolis Dynamics Approach

The time evolution of the Hamming distance (damage spreading) for the S=1/2 and S=1 Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to the temperature range for both models: a low-temperature one where the distance in the long-time limit is finite and seems not to depend on the initial distance and the system size; a high-temperature one where the distance vanishes in the long-time limit. Using the finite size scaling method, the dynamical phase transition (damage spreading transition) temperature is obtained as T_c≌1.675±0.025 for the S=1 Ising model.     

Spin current and its heat effect in a multichannel quantum wire with Rashba spin-orbit coupling

Using the perturbation method,we theoretically study the spin current and its heat effect in a multichannel quantum wire with Rashba spin-orbit coupling.The heat generated by the spin current is calculated.With the increase of the width of the quantum wire,the spin current and the heat generated both exhibit period oscillations with equal amplitudes.When the quantum-channel number is doubled,the oscillation periods of the spin current and of the heat generated both decrease by a factor of 2.For the spin current j s,xy,the amplitude increases with the decrease of the quantum channel;while the amplitude of the spin current j s,yx remains the same.Therefore we conclude that the effect of the quantum-channel number on the spin current j s,xy is greater than that on the spin current j s,yx.The strength of the Rashba spin-orbit coupling is tunable by the gate voltage,and the gate voltage can be varied experimentally,which implies a new method of detecting the spin current.In addition,we can control the amplitude and the oscillation period of the spin current by controlling the number of the quantum channels.All these characteristics of the spin current will be very important for detecting and controlling the spin current,and especially for designing new spintronic devices in the future.     

Anti-symmetry consideration on the preservation of entanglement of spin system

In this work we offer an approach to protect the entanglement based on the anti-symmetric property of the Hamiltonian. Our main objective is to protect the entanglement of a given initial three-qubit state which is governed by Hamiltonian of a three-spin Ising chain in site-dependent transverse fields. We show that according to anti-symmetric property of the Hamiltonian with respect to some operators mimicking the time reversal operator, the dynamics of the system can be effectively reversed. It equips us to control the dynamics of the system. The control procedure is implemented as a sequence of cyclic evolution; accordingly the entanglement of the system is protected for any given initial state with any desired accuracy and long-time. Using this approach we could control not only the multiparty entanglement but also the pairwise entanglement. It is also notable that in this paper although we restrict ourselves mostly within a three-spin Ising chain in site-dependent transverse fields, our approach could be applicable to any n$n$-qubit spin system models.     

Dynamical response of quantum spin-glass models at t = 0

We study the behavior of two archetypal quantum spin glasses at T = 0 by exact diagonalization techniques: the random Ising model in a transverse field and the random Heisenberg model. The behavior of the dynamical spin response is obtained in the spin-glass ordered phase. In both models it is gapless and has the general form chi(")(omega) = qdelta(omega)+chi(")(reg)(omega), with chi(")(reg)(omega) approximately omega for the Ising and chi(")(reg)(omega) approximately const for the Heisenberg, at low frequencies. The method provides new insight to the physical nature of the low-lying excitations.     

The compensation temperature study of the mixed Ising ferrimagnetic spin system with crystal field in a transverse field

Abstract. The magnetic properties of the nearest-neighbor interaction mixed spin-1/2 and spin-1 Ising ferrimagnetic spin system with crystal field in a transverse field are investigated within the framework of the effective-field theory. Particular emphasis is given to the honeycomb lattice with coordination number Z = 3 for which magnetizations are obtained. If transverse field Ω varies in the certain ranges, we find that the compensation temperature is obtained for the value of the crystal field D in a restricted region. We discuss in detail the influence of the transverse field on the behaviors of the compensation point and magnetization curves in this paper.     

Spin and energy coupling in the Ising model with a transverse field: One dimension,T=∞

The dynamics of the one dimensional Ising model with a transverse field is studied in the limit T = ∞. Numerical studies of the classical chain and exact calculations for the spin $\text{1}\text{2}$ chain indicate the presence of an energy density term in the dynamic spin susceptibility along the direction of the field.