Markov and stability properties of equilibrium states for nearest-neighbor interactions

Consider models on the lattice ^d with finite spin space per lattice point and nearest-neighbor interaction. Under the condition that the transfer matrix is invertible we use a transfer-matrix formalism to show that each Gibbs state is determined by its restriction to any pair of adjacent (hyper)planes. Thus we prove that (also in multiphase regions) translationally invariant states have a global Markov property. The transfer-matrix formalism permits us to view the correlation functions of a classicald-dimensional system as obtained by a linear functional on a noncommutative (quantum) system in (d – 1)-dimensions. More precisely, for reflection positive classical states and an invertible transfer matrix the linear functional is a state. For such states there is a decomposition theory available implying statements on the ergodic decompositions of the classical state ind dimensions. In this way we show stability properties of _ev ^d -ergodic states and the absence of certain types of breaking of translational invariance.     

Reduced Dirac-Kähler lattice fermion action

It is shown that the lattice Dirac-Kähler action is reducible under a chiral-like transformation. This provides a new lattice fermion action for spinors that have 2^d−1 components (instead of 2^d), with the property that, in the free case, each component satisfies the lattice euclidean Klein-Gordon equation. Reflection positivity is satisfied on the lattice, thus assuring a (positive) physical Hilbert space. In d = 4 dimensions the spinors have 8 components, and the correct physical chiral anomaly in the continuum limit. The action is suitable for QCD quarks which, in the continuum limit, are described by Dirac spinors that occur in flavor doublets.     

Mutual Annihilation of Two Diffusing Particles in One- and Two-Dimensional Lattices

The probabilistic dynamics of a pair of particles which can mutually annihilate in the course of their random walk on a lattice is considered and analytically found for d=1 and d=2. In view of available recent experiments achieved on the femtosecond scale, emphasis is put on the necessity of a full continuous-time, discrete-space solution at all times. Quantities of physical interest are calculated at any time, including the total pair survival probability N(t) and the two-particle correlation function. As a by-product, the lattice version allows for a precise regularization of the continuous-space framework, which is ill-conditionned for d2; this being done, formal generalization to any real dimensionality can be straightforwardly performed.     

Study of the magnetic and electronic properties of the Fe4N with pressure

In the present work, we report ab-initio studies of the magnetic property variations with pressure of both iron sites in the structure of Fe₄N, using full-potential linearized augmented plane wave method and the Perdew–Burke–Ernzerhof functional and generalized gradient approximation to describe the exchange-correlation potential are reported. The results show that the magnetic moment of FeI is almost constant while the magnetic moment of FeII presents a discontinuity when the lattice parameter is varied. This is reflected in the compression of the spin up and down energy bands to different concentration points. The variation in the FeII magnetization arises mainly from changes in the d_xy, d_xz, d_yz and d_x2−y2 orbitals.     

Existence of enantiomeric phase separation in a three-dimensional lattice gas model

A three-dimensional lattice gas model for enantiomeric phase separation is introduced. The enantiomeric molecules (d andl) are the two nonsuperimposable mirror images having the molecular structure C(AB)₂, where C is a tetrahedrally bonded carbon atom with one bond to each end of two AB groups. The lattice gas model consists of a body-centered cubic lattice, each site of which can be either vacant or occupied by a molecule oriented so that the A and B groups point toward neighboring lattice sites. Pairs of molecules interact with short-range, orientationally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove thatd-rich andl-rich phases exist in the model at sufficiently low temperature. For another domain of interaction parameters, at sufficiently high chemical potential there is an infinite number of ground states, each containing a racemic mixture ofd andl molecules.     

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, d≥1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.     

A mean spherical model with coulomb interactions. II. Correlations at a free surface

Studies of the mean spherical model with Coulomb interactions are continued, by considering a system on ad-dimensional lattice which is periodic ind–1 dimensions and has a free surface in the remaining dimension. It is shown explicitly that correlations along the free surface decay asy ^–d ind dimensions and show that the surface properties of this model are those expected for a charged system in its plasma phase.     

Generalizing the Cooper-pair instability to doped Mott insulators

Copper oxides become superconductors rapidly upon doping with electron holes, suggesting a fundamental pairing instability. The Cooper mechanism explains normal superconductivity as an instability of a fermi-liquid state, but high-temperature superconductors derive from a Mott-insulator normal state, not a fermi liquid. We show that precocity to pair condensation with doping is a natural property of competing antiferromagnetism and d-wave superconductivity on a singly-occupied lattice, thus generalizing the Cooper instability to doped Mott insulators, with significant implications for the high-temperature superconducting mechanism.     

Mesoscopic Two‐Dimensional Electron Crystals in Single and Double Layers

We present results of Monte‐Carlo simulations for finite 2D single and bilayer systems. Strong Coulomb correlations lead to arrangement of particles in configurations resembling a crystal lattice. For binary layers there exists a particularly rich variety of lattice symmetries which depend on the interlayer separation d. We demonstrate that in these mesoscopic lattices there exist two fundamental types of ordering: radial and orientational. The dependence of the melting temperature on d is analyzed and a stabilization of the crystal compared to a single layer is found.     

LRO in Lattice Systems of Linear Classical and Quantum Oscillators. Strong Nearest-Neighbor Pair Quadratic Interaction

For systems of one-component interacting oscillators on the d-dimensional lattice, d>1, whose potential energy besides a large nearest-neighbour (n-n) ferromagnetic translation-invariant quadratic term contains small non-nearest-neighbour translation invariant term, an existence of a ferromagnetic long-range order for two valued lattice spins, equal to a sign of oscillator variables, is established for sufficiently large magnitude g of the n-n interaction with the help of the Peierls type contour bound. The Ruelle superstability bound is used for a derivation of the contour bound.     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

Steps and facets at the surface of soft crystals

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found. Received 25 June 2001     

Exact solution of a vertex model ind dimensions

We consider a class of vertex models describing directed lines on a lattice in arbitraryd dimensions, and solve the model exactly for the Cartesian lattice and in the case that each loop of lines carries a fugacity - 1. Our analysis, which can be carried out for arbitrary lattices, is based on an equivalence of the vertex model with a dimer problem. The dimer problem is, in turn, solved using the method of Pfaffians. It is found that the system is frozen below a critical temperatureT _cwith the critical exponent = (3 –d)/2.     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.     

A rigorous bound on the critical exponent for the number of lattice trees,animals, and polygons

The number ofn-site lattice trees (up to translation) is believed to behave asymptotically asCn ^{–0 n} , where is a critical exponent dependent only on the dimensiond of the lattice. We present a rigorous proof that (d–1)/d for anyd2. The method also applies to lattice animals, site animals, and two-dimensional self-avoiding polygons. We also prove that v whend=2, wherev is the exponent for the radius of gyration.     

Self-avoiding walk model for proteins

We study a model for the backbone of proteins on a square lattice which consists of the path traced out by a self-avoiding walk (SAW) on the lattice and bridges not belonging to sites on the SAW but connecting nearest neighbor sites of the SAW. We calculated the fractal dimensiond _w for random walk on this model and found thatd _w2.6, in disagreement with a recent suggestion thatd _w should be 2.     

Cluster expansion ford-dimensional lattice systems and finite-volume factorization properties

We consider classical lattice systems with finite-range interactions ind dimensions. By means of a block-decimation procedure, we transform our original system into a polymer system whose activity is small provided a suitable factorization property of finite-volume partition functions holds. In this way we extend a result of Olivieri.     

First-principles electronic structure of rare-earth arsenides

The electronic properties of rare-earth arsenides have been calculated from first principles. In the calculations we have treated the rare-earth f electrons both as core-like and as valence-like electrons. We consider the changes in the energy bands and in the density of states near the Fermi level which are found to be relevant, except for the case of LuAs, and discuss this in relation with the role played from the rare-earth 5d derived states. Moreover we show that the rare-earth 5d related bands are particularly sensitive to the variation of the lattice constant; change in the lattice constant of less than 1% leads to a different behaviour with respect to the crossing of the rare-earth 5d derived bands and the As 4p derived bands along the Δ-direction. This point is discussed in connection with the possibility of having a semimetal-semiconductor transition in the rare-earth arsenides. Received 22 February 2001     

Lyapunov Bounds for Lattice Gauge Dynamics

We study the classical Hamiltonian dynamics of the Kogut–Susskind model for lattice gauge theories on a finite box in a d-dimensional integer lattice. The coupling constant for the plaquette interaction is denoted λ². When the gauge group is a real or a complex subgroup of a unitary matrix group U(N), N≥ 1, we show that the maximal Lyapunov exponent is bounded by , uniformly in the size of the lattice, the energy of the system as well as the order, N, of the gauge group. Received: 20 December 1997 / Accepted: 21 July 1998     

Configurational statistics of densely and fully packed loops in the negative-weight percolation model

By means of numerical simulations we investigate the configurational properties of densely and fully packed configurations of loops in the negative-weight percolation (NWP) model. In the presented study we consider 2d square, 2d honeycomb, 3d simple cubic and 4d hypercubic lattice graphs, where edge weights are drawn from a Gaussian distribution. For a given realization of the disorder we then compute a configuration of loops, such that the configurational energy, given by the sum of all individual loop weights, is minimized. For this purpose, we employ a mapping of the NWP model to the “minimum-weight perfect matching problem” that can be solved exactly by using sophisticated polynomial-time matching algorithms. We characterize the loops via observables similar to those used in percolation studies and perform finite-size scaling analyses, up to side length L = 256 in 2d, L = 48 in 3d and L = 20 in 4d (for which we study only some observables), in order to estimate geometric exponents that characterize the configurations of densely and fully packed loops. One major result is that the loops behave like uncorrelated random walks from dimension d = 3 on, in contrast to the previously studied behavior at the percolation threshold, where random-walk behavior is obtained for d ≥ 6.