Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field

We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with linear friction. Spatial couplings and the dissipative dynamics combine to form a new quantum criticality which is independent of dissipation strength.     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

横场中非束缚类准周期伊辛链的赝临界点

本文系统地研究了有限尺寸下非束缚类准周期量子伊辛链在横场中的赝临界点的行为. 首先, 通过计算平均磁矩和协作参量, 发现这两个量的导数随着横场的变化都会出现两个清晰的峰. 这与束缚类伊辛链和无序伊辛链的结果明显不同. 其次, 研究了横场中赝临界点的概率分布情况, 发现概率分布并不是高斯型的. 这也与无序的结果不同. 最后, 分析了赝临界点产生的原因, 发现赝临界点是由非束缚类准周期伊辛链中的集团结构造成的.     

Universal,finite-temperature,crossover functions of the quantum transition in the Ising chain in a transverse field

We consider finite-temperature properties of the Ising chain in a transverse field in the vicinity of its zero-temperature, second-order quantum phase transition. New universal crossover functions for static and dynamic correlators of the “spin” operator are obtained. The static results follow from an early lattice computation of McCoy, and a method of analytic continuation in the space of coupling constants. The dynamic results are in the “renormalized classical” region and follow from a proposed mapping of the quantum dynamics to the Glauber dynamics of a classical Ising chain.     

On the thermodynamics of the random one-dimensional Ising chain in a transverse field

For three simple one-dimensional disordered models: (a) the Ising chain with random magnetic moments in a transverse field, (b) the Ising chain with random coupling constants in a transverse field, and (c) the X-Y model with a special type of disorder, the asymptotic equivalence in the thermodynamic limit is proved and some of its consequences are discussed. The spectral density of the finite chain for the model (a) is calculated by Dean's method for several representative cases and the presence of the local modes is indicated. The expressions for the initial susceptibilities for the models (a) and (b) are reviewed and (in two cases) the derivations are simplified.     

Effect of intersite repulsion on the correlation functions and thermodynamics of an Ising chain with annealed magnetic disorder

An exact solution for a model describing the equilibrium behavior of an ensemble of Ising chains with nonmagnetic intersite repulsion of nearest neighbors and an equilibrium distribution of nonmagnetic impurities is obtained using the transfer matrix technique. The possibility of exciting quantum phase transitions using the intersite repulsion parameter in a system is demonstrated. Proximity to the critical points of these transitions has a substantial effect on the temperature dependence of a system’s magnetic susceptibility.     

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.     

The quantum compass chain in a transverse magnetic field

We study the magnetic behaviors of a spin-1/2 quantum compass chain (QCC) in a transverse magnetic field, by means of the analytical spinless fermion approach and numerical Lanczos method. In the absence of the magnetic field, the phase diagram is divided into four gapped regions. To determine what happens by applying a transverse magnetic field, using the spinless fermion approach, critical fields are obtained as a function of exchanges. Our analytical results show, the field-induced effects depend on in which one of the four regions the system is. In two regions of the phase diagram, the Ising-type phase transition happens in a finite field. In another region, we have identified two quantum phase transitions (QPT)s in the ground state magnetic phase diagram. These quantum phase transitions belong to the universality class of the commensurate-incommensurate phase transition. We also present a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. In particular, we show that the intermediate state (h _c1 < h < h _c2) is gapful, describing the spin-flop phase.     

Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal (H$H$) and transverse (Ω$\Omega$) magnetic fields. Using the effective-field theory (EFT) with correlation in single site clusters we calculate the phase diagrams in the H−T$H-T$ and Ω−T$\Omega -T$ planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.     

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.     

Linear chain of spins in an inhomogeneous transverse magnetic field

The energy spectrum of the quasiparticles of a one-dimensional chain of half-integral spins with a simple form of interaction, situated in an inhomogeneous magnetic field, is calculated in second-order perturbation theory. It is shown that the mixing of the levels is proportional to the squares of the perturbing inhomogeneities of the field. It is shown that, for a sufficiently large mean value of the magnetic field, the shift of the levels relative to their unperturbed values is symmetric. For small mean values of the magnetic field the higher levels are shown to shift to a greater degree than those situated closer to the ground state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 26–29, February, 1972.     

The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc

The form-factor bootstrap approach is used to compute the exact contributions in the large-distance expansion of the correlation function 〈σ(x)σ(0)〉 of the two-dimensional Ising modeliin a magnetic field at T = T_c The matrix elements of the magnetization operator σ,(x) present a rich analytic structure induced by the (multi-)) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.     

Ising model in a transverse random field

The transverse random-field Ising model with a trimodal distribution is studied within mean-field and mean-field renormalization-group approaches. The phase diagram is obtained and all the transition lines are second order. An ordered phase persists for large random fields provided that the probability of the zero transverse field is greater than the site-percolation threshold.