Strongly coupled Ising chain under a weak random field (original) (raw)

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.

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

Random quantum Ising chains with competing interactions

Physical Review E, 2005

In this paper we discuss the criticality of a quantum Ising spin chain with competing random ferromagnetic and antiferromagnetic couplings. Quantum fluctuations are introduced via random local transverse fields. First we consider the chain with couplings between first and second neighbors only and then generalize the study to a quantum analog of the Viana-Bray model, defined on a small world random lattice. We use the Dasgupta-Ma decimation technique, both analytically and numerically, and focus on the scaling of the lattice topology, whose determination is necessary to define any infinite disorder transition beyond the chain. In the first case, at the transition the model renormalizes towards the chain, with the infinite disorder fixed point described by Fisher. This corresponds to the irrelevance of the competition induced by the second neighbors couplings. As opposed to this case, this infinite disorder transition is found to be unstable towards the introduction of an arbitrary small density of long range couplings in the small world models.

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.

Theory of the Random Field Ising Model

Series on Directions in Condensed Matter Physics, 1997

A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

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.

Long-time behavior for the 1-D stochastic Ising model with unbounded random couplings

2003

We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged spin auto-correlation function has an exponential decay in time. We prove that, if the couplings are unbounded, the decay switches to either a power law or a stretched exponential, in general.

A ferromagnetic chain in a random weak field

Journal of Physics Condensed Matter, 1996

The harmonic magnon modes in a Heisenberg ferromagnetic chain in a random weak field are studied. The Lyapunov exponent for the uniform (k = 0) mode is computed using the coherent potential approximation (CPA) in the weak-disorder limit. The CPA results are compared with the numerical and weak-disorder expansions of various random systems. We have found that the inverse localization length and the integrated density of states have anomalous power law behaviour as reported earlier. The CPA also reproduces the dispersion law for the same system, calculated by Pimentel and Stinchcombe using the real space renormalization scaling technique. A brief comment is also made for the uniform weak-field case.

Coupled Ising models with disorder

Journal of Physics A: Mathematical and General, 2000

In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analyzed by help of Monte Carlo simulations and field theory arguments.