Dynamics of the random one-dimensional transverse Ising model (original) (raw)

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

Physica A-statistical Mechanics and Its Applications, 1977

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

Transverse-field Ising spin chain with inhomogeneous disorder

We consider the critical and off-critical properties at the boundary of the random transversefield Ising spin chain when the distribution of the couplings and/or transverse fields, at a distance l from the surface, deviates from its uniform bulk value by terms of order l −κ with an amplitude A. Exact results are obtained using a correspondence between the surface magnetization of the model and the surviving probability of a random walk with time-dependent absorbing boundary conditions. For slow enough decay, κ < 1/2, the inhomogeneity is relevant: Either the surface stays ordered at the bulk critical point or the average surface magnetization displays an essential singularity, depending on the sign of A. In the marginal situation, κ = 1/2, the average surface magnetization decays as a power law with a continuously varying, A-dependent, critical exponent which is obtained analytically. The behavior of the critical and off-critical autocorrelation functions as well as the scaling form of the probability distributions for the surface magnetization and the first gaps are determined through a phenomenological scaling theory. In the Griffiths phase, the properties of the Griffiths-McCoy singularities are not affected by the inhomogeneity. The various results are checked using numerical methods based on a mapping to free fermions. 05.50.+q, 64.60.Fr, 68.35.Rh

Dynamical behavior of the random-bond transverse Ising model with four-spin interactions

Physical Review B, 2000

We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. We analyze how the presence of disorder affect the dynamical behavior of the system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced. Such crossover is also present in the case of an increase in bond dilution.

Renormalization group study of the two-dimensional random transverse-field Ising model

Physical Review B, 2010

The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to L = 2048. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: ν = 1.24(2). For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: x = 0.982(15) and ψ = 0.48(2). We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.

Quantum Ising model in a transverse random field: A density-matrix renormalization-group analysis

Physical Review B, 1997

The spin-1/2 quantum Ising chain in a transverse random magnetic field is studied by means of the density-matrix renormalization group. The system evolves from an ordered to a paramagnetic state as the amplitude of the random field is increased. The dependence of the magnetization on a uniform magnetic field in the z direction and the spontaneous magnetization as a function of the amplitude of the transverse random magnetic field are determined. The behavior of the spin-spin correlation function both above and at criticality is studied. The scaling laws for magnetization and correlation functions are tested against previous numerical and renormalization-group results.

Dynamical properties of random-field Ising model

Physical Review E, 2013

Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter and the spin-spin correlation functions are studied in the non equilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two dimensional random field Ising model possesses long range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long range order in the system.

Ground-state correlations and finite temperature properties of the transverse Ising model

The European Physical Journal B, 2005

We present a semi-analytic study of Ising spins on a simple square or cubic lattice coupled to a transverse magnetic field of variable strength. The formal analysis employs correlated basis functions (CBF) theory to investigate the properties of the corresponding N-body ground and excited states. For these states we discuss two different ansaetze of correlated trial wave functions and associated longitudinal and transverse excitation modes. The formalism is then generalized to describe the spin system at nonzero temperatures with the help of a suitable functional approximating the Helmholtz free energy. To test the quality of the functional in a first step we perform numerical calculations within the extended formalism but ignore spatial correlations. Numerical results are reported on the energies of the longitudinal and the transverse excitation modes at zero temperature, on critical data at finite temperatures, and on the optimized spontaneous magnetization as a function of temperature and external field strength.

Critical temperature and density of spin flips in the anisotropic random-field Ising model

Physical Review B, 1998

We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average chain free energy ("chain meanfield" approach). The free energy is found using a mapping on a Brownian motion model. We calculate the order parameter and give expressions for the critical random magnetic field strength below which the ground state exhibits long range order and for the critical temperature as a function of the random magnetic field strength. In the limit of vanishing interchain interactions, we obtain corrections to the zero-temperature estimate by Imry and Ma [Phys. Rev. Lett. 35, 1399] of the ground state density of domain walls (spin-flips) in the one-dimensional random field Ising model. One of the problems to which our model has direct relevance is the lattice dimerization in disordered quasi-one-dimensional Peierls materials, such as the conjugated polymer trans-polyacetylene.

Temperature effects on the dynamics of the 1-D transverse Ising model with four-spin interactions

Physica A-statistical Mechanics and Its Applications - PHYSICA A, 2004

The dynamics of one-dimensional quantum spin systems has been a long standing theoretical and experimental problem. Among them, the transverse Ising model with multi-spin interactions, regarded as one of the simplest with non-trivial dynamics, has attracted considerable interest in recent years. We investigate the temperature effects on the dynamics of the transverse Ising model with four-spin interactions. The model is relevant to the physics of poly(vinylidene fluoride-trifluoroethylene)[P(VDF-TrFE)] copolymers. We determine the time-dependent correlation function and spectral density for all temperatures for cases where the transverse field B is less, equal or greater than the four-spin coupling J. Our calculations were done with rings of up to 11 spins. However the results presented are also valid in the thermodynamic limit. We find that the time-dependent correlation function in general has oscillatory behavior when the transverse field is stronger than the coupling energy. On ...