Wetting phenomena in the two-dimensional ANNNI model in a field

Wetting phenomena at various interface types in the ordered phases of the two-dimensional axial next-nearest neighbour Ising (or ANNNI) model in a field are studied using a transfer matrix approach and Monte Carlo techniques. Different types of wetting at distinct wetting lines or at the bulk phase boundary are identified, which may be tested experimentally in adsorbate systems with a (p×1) ordering, forp equal to two, three or four.     

Extended dynamical mean field theory study of the periodic Anderson model

We investigate the competition of the Kondo and the RKKY interactions in heavy fermion systems. We solve a periodic Anderson model using extended dynamical mean field theory (EDMFT) with quantum Monte Carlo method. We monitor simultaneously the evolution of the electronic and magnetic properties. As the RKKY coupling increases the heavy fermion quasiparticle unbinds and a local moment forms. At a critical RKKY coupling there is an onset of magnetic order. Within EDMFT the two transitions occur at different points and the disappearance of the magnetism is not described by a local quantum critical point.     

An analytically soluble model for the mean field theory of collisions

A variational principle is used for the calculation of the matrix element of a resolvent operatot (E-H)^-1. Trial functions restricted to products of single particle orbitals generate driven, Hartree-Fock-like equations, with a right-hand side. We find a soluble model where these nonlinear equations reduce to the search for the roots of a 5th degree polynomial. One of the roots is always acceptable and generates an excellent numerical approximation. The theory has a regular on-shell limit.     

The two-dimensional ANNNI model in the CVM approximation

The phase diagram of the two-dimensional ANNNI model is investigated by the cluster variation method (CVM). We confirm the stability of the disordered phase down toT=0 and the absence of a Lifshitz point at finite temperature forK<1/2, whereK the ratio of the second to the first neighbor pair interactions. Two different modulation regimes for the correlation functions of the disordered phase are separated by a disorder line along which theq vector of the susceptibility maximum undergoes a lock-in transition. The study in reciprocal space of the stability of the disordered phase allows us to define a critical line in the phase diagram along which theq vector characterizing the instability is incommensurate. Finally, we show the existence of another Lifshitz point forK tending to infinity.     

Rectangular lattice gas model with competing interactions and the two-dimensional ANNNI model in a field

A lattice gas model with short range competing interactions for adsorption on (110) surfaces of fcc crystals, in particular for O/Pd(110), as well as its Ising analog, the two-dimensional ANNNI model with antiferromagnetic axial nearest and next-nearest neighbour interactions in a field, are studied using the free fermion approximation and Monte Carlo techniques. The phase diagrams display different commensurate phases and incommensurate regions. Static and dynamic aspects of topological defects (walls and dislocations) characterising the incommensurate structures are investigated.     

Dynamic mean field theory of the SK-spin glass

The dynamic infinite range SK model for a spin glass is generalized by considering the bonds as slowly time-dependent. This allows to regularize the long-time behaviour even in the thermodynamic limit, contrary to the corresponding treatment by Sompolinsky and Zippelius. Depending on the order in which limits are taken the model describes annealed or quenched disorder. Below the Almeida-Thouless border of stability the solution found by Sompolinsky and Zippelius is unique unless causality or homogeneity in time are violated.     

Dynamic mean field theory of the SK-spin glass

The ground state of the holmium ion in ferromagnetic HoAl₂ is discussed in the light of available experimental evidence, including hitherto unpublished NMR measurements on¹⁶⁵Ho. The measured quadrupole splitting is not consistent with the ground state derived from neutron form factor experiments, but is compatible with exchange and crystal field parameters derived from magnetization measurements and neutron spectroscopy in the context of the conventional three-parameter mean-field model. A more detailed analysis of the NMR data indicates that the exchange interaction in HoAl₂ is over 20% stronger than that derived, using mean-field theory, from the Curie temperature. Using the revised exchange constant and a weighted average of published crystal field parameters, we obtain = (9.39 ± 0.05) _B for the moment on the Ho³⁺ ion atT =0. The contribution of orbitally polarized conduction electrons to the hyperfine field at the holmium nucleus is estimated to be (–1.4±2.0) T.     

Finite-size behaviour of the two-dimensional ANNNI model

The two-dimensional axial next-nearest neighbour Ising (ANNNI) model of finite size with periodic boundary conditions is studied by the Monte Carlo method. The model shows an interesting finite size dependence in connection with its oscillatory correlations pretending for finite systems a Lifshitz point in one part of the phase diagram, while the infinite system appears to display one in another part of the phase diagram.     

The one-dimensional ANNNI model in a transverse field: analytic and numerical study of effective Hamiltonians

We consider a quantum spin-1/2 Ising chain with competing nearest and next-nearest neighbor interactions in a transverse magnetic field, which is known to be equivalent to the classical two-dimensional ANNNI model. Within a perturbation theory for small transverse field (corresponding to low temperatures in the classical ANNNI model) we derive two effective Hamiltonians: the free model describing free fermions on a fictitious lattice that excludes particular heavy excitations of the original system; and the complete model, which incorporates creation and annihilation of these fermions. Whereas the former possesses only three phases (ferromagnetic, floating and anti phase), the latter contains the full physics of the 2d ANNNI model, including a paramagnetic phase between the ferromagnetic and floating phase and a Kosterlitz-Thouless transition. New analytic results are derived for the free model, e.g. the excitation spectrum that turns out to be non-trivial. Our effective Hamiltonians are defined on a restricted Hilbert space so that exact diagonalization calculations can be done for much larger system sizes. Results from extensive Lanczos calculations for system sizes up to L = 32 are presented confirming the original predictions from Villain and Bak.     

Incommensurate structure in the lattice-gas ANNNI model

The phase diagram of the two-dimensional lattice-gas ANNNI model is investigated using the cluster transfer-matrix method. The numerical calculations have shown commensurate, disordered, and floating incommensurate phases. The properties of the incommensurate phase are studied in detail and the position of the Lifshitz point is discussed.     

The 1/N-expansion as a perturbation about the mean field theory: A one-dimensional fermi model

We examine a family of probability measures onR ^L with real parameter >0 and integer parametersN,L>0. Each such measure is equivalent to the lattice version of a one-dimensional discrete chiral-invariant fermionic quantum field theory with quartic interaction, withN the number of flavours. After applying the Matthews-Salam formula, the model becomes a statistical mechanical model of a chain of continuous Gaussian spins, coupled with a certain non-standard weight function. Finally, the model can also be considered as a probability measure on the set of tridiagonal matrices with fixed off-diagonal and random diagonal entries.Our analysis shows how to develop an asymptotic expansion in 1/N, valid for allL and , for the fundamental expectation values. From this it follows that the two point fermion correlation function decays with a mass which agrees to the leading order in 1/N with the mean field value calculated by the argument of Gross-Neveu. The analytical technique we develop in essence combines a transfer matrix method with the Laplace method (steepest descent) for asymptotics of integrals.Partially supported by FAPESP and CNPq.Partially supported by CNPq.Supported by the Natural Sciences and Engineering Research Council of Canada.     

Dynamical phase transitions in the two-dimensional ANNNI model

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly see several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.     

Dynamic mean field theory of the SK spin glass

The existence of a great number of low-temperature phases in the SK-model of a spin glass and their ultrametric organization appears generally accepted and has been obtained by various techniques. In all cases it can be traced back to ultrametric features in the respective ansatz used. Within dynamic mean field theory I have investigated two situations in which the validity of such an ansatz can be controlled or is not made. In both cases I find only a trivial form of ultrametricity. Especially for an adiabatically cooled SK-spin glass in a small external field a single state appears to dominate below the AT-line. The transition occurs via exchange of stability rather than bifurcation, the scenario common to most other continuous phase transition. The results presented contradict the common belief.     

Transfer matrix analysis of the two-dimensional ANNNI model

The two-dimensional axial next-nearest neighbour Ising (ANNNI) model is studied for the first time by a transfer matrix method for semi-infinite strips (N×;N13). One obtains the thermodynamic properties and, more important, the correlation functions, which display directly the various magnetic structures. In one part of the phase diagram where a disorder line is believed to follow closely the ferromagnetic transition line the critical exponents appear to deviate from the expected ones. ForN13 a variational procedure is proposed.     

Cluster dynamical mean field theory of the Mott transition

We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.     

On the dynamic mean field theory of spin glasses

We derive in detail Sompolinsky's mean field theory of spin glasses using a diagram expansion of the effective local Langevin equation of Sompolinsky and Zippelius. We use a simpler generating functional than in the literature, on which the quenched average is very easily done. We pay special attention to the existence of an external field. We show that there are two different types of singularities for ω=0 in the equations. The first type, which leads to Parisi'sq(0), is connected with the local magnetisation. The second type, which leads toq′(x), is connected with the nonergodic behaviour. We show that the continuous limit of discrete Sompolinsky solutions has to be taken in order to be in accordance with the fluctuation dissipation theorem on infinite time scales. We discuss carefully the question of dynamical stability. We show that Sommers' solution is unstable only on an infinite time scale and thus remains an acceptable equilibrium theory with a broken symmetry. We argue that for ω=0 a formal violation of the fluctuation dissipation theorem is physically expected if the relaxation times are of the order of the switching time of the external field. From this point of view the spin-glass state is a steady state but not a real equilibrium state.     

On the mean field theory bound on the magnetization

The mean field bound on magnetization is proved for a class of one-component ferromagnetic systems and forD components systems with arbitraryD.