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.     

Surface excitations for the Ising model in a transverse field

We employ a microscopic theory to discuss the excitation spectrum of a semi-infinite spin system (or pseudo-spin system) described by the Ising model in a transverse field. It is shown that under certain conditions localised surface spin waves may exist, as well as the usual bulk spin waves.     

On the dynamics of the Ising model in a transverse field

Including mode coupling terms we give the equation of motion for the classical version of the transverse Ising model. The critical behaviour for d ? 2 is dominated by the mode coupling terms. The corresponding kinetic coefficient diverges with $\text{z =}\text{1}\text{2}\text{(d ? 2)}$. For 2 < d ? 4 the model behaves like a relaxator model.     

Phase transitions in the Ising model with transverse field

We show the existence of a phase transition in the Ising model with transverse field for dimensionsv 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.     

Purely quadrupolar spin-1 Ising model in a transverse field

A quantum Ising-like spin-1 model characterized by quadrupolar interaction, coupled to an external anisotropic field with both dipole and quadrupole momenta is analyzed. The general phase diagram (including temperature), as well as order parameter, specific heat, and susceptibility are evaluated in the mean-field approximation and exibit a rich structure with transitions of 2° and 1° order and tricritical points. ForT=0 the phase diagram is examined also by a recently formulated improved version of mean-field theory which has the usual mean-field theory as its zero-th order approximation.     

Quantum domain walls in the one-dimensional Ising model in a transverse field

Within the exactly soluble spin-$\text{1}\text{2}$ Ising chain in a transverse field, wavefunctions are identified which correspond to the domain wall-type solutions in the related classical model. For these wavefunctions the energy expectation values and longitudinal spin correlations are evaluated exactly. The results are used to comment on the relation between the quantum and classical domain walls.     

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

Phase diagrams and magnetization curves of a diluted spin-3/2 transverse Ising model in a random field on honeycomb lattices are investigated by the use of an effective-field theory with correlations. The tricritical point is found in the system, in contrast to the corresponding spin-1/2 Ising counterpart. The possible reentrant phenomena displayed by the system due to the competition effects that occur for appropriate ranges of the random and transverse fields are investigated.     

Cluster fermionic Ising spin glass model with a transverse field

The fermionic Ising spin glass (SG) model in the presence of a transverse magnetic field Γ is studied within a cluster mean field theory. The model considers an infinite-range interaction among magnetic moments of clusters with a short-range ferromagnetic intracluster coupling J₀. The spin operators are written as a bilinear combination of fermionic operators. In this quantum SG model, the intercluster disorder is treated by using a framework of one-step replica symmetry breaking (RSB) within the static approximation. The effective intracluster interaction is then computed by means of an exact diagonalization method. Results for several values of cluster size n_s, Γ and J₀ are presented. For instance, the specific heat can show a broad maximum at a temperature T^∗ above the freezing temperature T_f, which is characterized by the intercluster RSB. The difference between T^∗ and T_f is enhanced by Γ, which suggests that the quantum effects can increase the ratio T^∗/T_f. Phase diagrams (T versus Γ) show that the critical temperature T_f(Γ) decreases for any values of n_s and J₀ when Γ increases until it reaches a quantum critical point at some value of Γ_c.     

Infinite range Ising spin glass model with a transverse field

The infinite range Ising spin glass model with a transverse field is studied by the pair approximation extended to include quantum effects. A mean field equation is obtained and the transition temperature T_c is shown to increase linearly with the transverse field Γ when Γ is small.     

Renormalization and scaling of a two-dimensional Ising system in a transverse field at Tc>0

A quantum generalization of the Niemeijer and van Leeuwen (N-vL) renormalization group transformation is constructed which allows to study the critical properties (at T_c>0) of a two-dimensional Ising system with a transverse field on a triangular lattice. Explicit calculations are performed in a second order cumulant expansion. Only one fixed point is found corresponding to the same Ising-like hamiltonian given by N-vl. The linearized transformation has a zero eigenvalue associated with Γ, the transverse field strength. The critical properties of the system are briefly discussed; in particular we show that the singular behaviour of the transverse susceptibility at Γ = 0, which turns out to be of the same kind as that of the energy density, is explained by the existence of such a zero eigenvalue. Our arguments suggest a natural extension of this result to three dimensions.     

Classial and quantum solitons in the transverse field Ising model

We investigate the shape and the dynamics of domain walls in the one-dimensional Ising model with spin S, exchange constant J and external transverse field Γ using numerical calculations up to S = 20 and analytical approximations. For $\tfrac{\Gamma } {{JS}}$ \] we describe classical domain walls as strongly localized excitations, which have either central spin or central bond symmetry. These symmetries are identified also in the quantum case, when solitary excitations develop into energy bands. In the classical limit S → ∞ localization results from the exponential vanishing of the bandwidth for the lowest bands. We describe the relation between the spectrum of moving classical solitons and the quantum band structure.     

Renormalization group analysis of a constrained Ising model

A Hamiltonian formulation is used to describe a constrained Ising system which has a non-gaussian tricritical point and renormalized Ising critical exponents. Renormalization group analysis reveals the fixed points which characterize this behavior.     

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.     

Diluted transverse Ising model within the mean field renormalization group

Clusters of different size and symmetry are exploited in the study of the diluted transverse Ising model on several lattices within the mean field renormalization group approach. It is noticed that the critical exponents depend both on the size of clusters as well as on the cluster symmetry. Harris' conjecture is verified for all lattices studied.     

An exact result for the 1D random Ising model in a transverse field

It is shown exactly that for an N-site cyclic chain with hamiltonian H = ?Σ^N_i=1(γ_iS^x_i + J_iS^z_iS^z_iS^z_i+1), the gap in the excitation spectrum goes to zero when N → ∞ at the “critical point” given by the relation Π^N_i=1Γ_i = Π^N_i=1J_i.     

Ornstein-Zernike decay in the ground state of the quantum Ising model in a strong transverse field

We consider the quantum mechanical Ising ferromagnet in a strong transverse magnetic field in nay number of dimensions,d. We prove that in the ground state the power law correction to the exponential decay of the two point function isd/2. The proof begins by writing the ground state as a classical system in one more dimension. (Thus the classical Ornstein-Zernike power of (d-1)/2 becomesd/2). We then develop a convergent polymer expansion and use the techniques of Bricmont and Fröhlich [5].