Diffusion in lattice Lorentz gases : Nearest scatterers approximation

The expressions for diffusion coefficients and for velocity autocorrelation functions of lattice Lorentz gases are derived both in the nearest scatterers and Boltzmann approximations. The results are obtained for linear chain, square, triangular, simple cubic, body centred cubic, face centred cubic and face centred hyper cubic lattices. The diffusion coefficients are compared with those from the effective medium approximation for the square lattice and with computer simulation results for triangular, simple cubic and body centred cubic lattices.     

Metal-insulator transition in the Hubbard model with incommensurate magnetic structures

The metal-insulator transition for the square, simple cubic, and body centered cubic lattices has been studied within the Hubbard model at half-filling taking into account nearest- and next-nearest-neighbor electron hopping. Both staggered antiferromagnetic and incommensurate magnetic states (spin-spiral wave) have been considered. The inclusion of the latter states for the three-dimensional lattices does not change the general pattern of the metal-insulator transition, but opens the fundamentally new possibility of the metal-insulator transition of the first order between the magnetically ordered states for the square lattice.     

A lattice model for a real substance

A linear, a plane square, and a simple cubic hard core lattice model are treated by a mean-field approximation combined with a combinatorial approach. Assuming a hard core interaction between nearest-neighbor lattice sites and a rather arbitrary soft pair interaction between lattice sites placed at longer distances from one another, inert-gas-like phase diagrams can be constructed for suitable chosen combinatorial ansatzes.     

Transition from a two-dimensional superfluid to a one-dimensional Mott insulator

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.     

Lattice animals: A fast enumeration algorithm and new perimeter polynomials

A fast computer algorithm for enumerating isolated connected clusters on a regular lattice and its Fortran implementation are presented. New perimeter polynomials are calculated for the square, the triangular, the simple cubic, and the square lattice with next nearest neighbors.     

Influence of a uniform driving force on tracer diffusion in a one-dimensional hard-core lattice gas

The influence of a uniform driving force on tracer diffusion is investigated for a one-dimensional lattice gas where particles jump stochastically to unoccupied neighboring sites. A new, simple calculation is presented for the diffusion coefficient of a tracer particle with respect to its average drift, obtained recently by rigorous methods by De Masi and Ferrari. A theoretical expression describing the tracer particle mean square displacement approximately for all times is derived and found to be in excellent agreement with the results of Monte Carlo simulations.     

Roughening behavior of a one-dimensional crystal surface with inverse square potential

The discrete Gaussian chain with inverse square potential—which models a one-dimensional crystal surface—is studied by Monte-Carlo methods. The system is found to undergo a roughening transition, and the temperature-dependent correlation function exponent η(T) is shown to be discontinous at the critical point. These results can be transposed to the metal-insulator transition of a one-dimensional plasma of logarithmically interacting charges.     

Excitonic metal–insulator phase transition of the Mott type in compressed calcium

It has been experimentally found that, under the static compression of a calcium crystal at room temperature, it undergoes a series of structural phase transitions: face-centered cubic lattice → body-centered cubic lattice → simple cubic lattice. It has been decided to investigate precisely the simple cubic lattice (because it is an alternative lattice) with the aim of elucidating the possibility of the existence of other (nonstructural) phase transitions in it by using for this purpose the Hubbard model for electrons with half-filled ns-bands and preliminarily transforming the initial electronic system into an electron–hole system by means of the known Shiba operators (applicable only to alternative lattices). This transformation leads to the fact that, in the new system of fermions, instead of the former repulsion, there is an attraction between electrons and holes. Elementary excitations of this new system are bound boson pairs—excitons. This system of fermions has been quantitatively analyzed by jointly using the equation-of-motion method and the direct algebraic method. The numerical integration of the analytically exact transcendental equations derived from the first principles for alternative (one-, two-, and three-dimensional) lattices has demonstrated that, in systems of two-species (electrons + hole) fermions, temperature-induced metal–insulator phase transitions of the Mott type are actually possible. Moreover, all these crystals are in fact excitonic insulators. This conclusion is in complete agreement with the analytically exact calculations of the ground state of a one-dimensional crystal (with half-filled bands), which were performed by Lieb and Wu with the aim to find out the Mott insulator–metal transition of another type.     

Absence of re-entrant phase transition of the antiferromagnetic Ising model on the simple cubic lattice: Monte Carlo study of the hard-sphere lattice gas

We perform Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, z_c = 1.0588 ± 0.0003. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice.     

Different kinds of discrete breathers in a Sine-Gordon lattice

We study a one-dimensional Sine-Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the one-dimensional Sine-Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.     

Random sequential adsorption on a ladder

We study the asymptotic coverage of a lattice to which particles are randomly and irreversibly attached, under the constraint of nearest neighbor exclusion. After reviewing the case of a one-dimensional lattice, we extend the treatment first to a triangular ladder and then to a square ladder. The former maps onto a previously solved one-dimensional case, the latter does not. We also determine the time-dependent coverage of the square ladder. Implications as to the process on a full 2-dimensional square lattice are discussed.     

Efficient Implementation of the Pivot Algorithm for Self-avoiding Walks

The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures and algorithms used, and provide a heuristic argument that the mean time per attempted pivot for N-step self-avoiding walks is O(1) for the square and simple cubic lattices. Numerical experiments conducted for self-avoiding walks with up to 268 million steps are consistent with o(log N) behavior for the square lattice and O(log N) behavior for the simple cubic lattice. Our method can be adapted to other models of polymers with short-range interactions, on the lattice or in the continuum, and hence promises to be widely useful.     

Superfluidity of a perfect quantum crystal II

This paper continues the work begun in a previous paper [Eur. Phys. J. B 71, 85 (2009)]. To treat the equations that describe a crystal with condensate that can be superfluid, a method termed the Kirkwood approximation is used. Earlier, the method was found to be rather seminal when applied to a classical crystal. In the case of a simple cubic lattice, solutions to the equations under study can be expressed in terms of the well-known Mathieu functions. A more realistic case of the face centered cubic lattice is also considered although in this case the three-dimensional equations cannot be reduced to one-dimensional ones. Condensate crystals without superfluidity are studied first and then the same crystals in a superfluid state. It is shown in particular that a crystal in which the condensate is formed is energetically preferable with respect to the same quantum crystal without condensate at absolute zero of temperature. Therefore, on lowering the temperature there must somewhere occur Bose-Einstein condensation in the crystal. In the concluding section, we discuss various physical aspects of the problem.     

Solitons in a diatomic chain with competing nonlinearities

A one-dimensional diatomic chain whose energy contains cubic and quartic terms in the atomic displacements is considered. A modified asymptotic method is proposed for finding soliton solutions to equations describing systems with nonlinearities of various symmetry. It is shown that the dynamics of the model in question can be described in terms of equations that are similar to the dynamic equations for a diatomic chain with an even potential function. Soliton solutions of a new, unusual type are found in the specific case of a free diatomic chain with a purely cubic anharmonic potential.     

Site-bond percolation problems

We study a percolation process in which both sites and bonds are randomly blocked, independent of each other. In the Bethe lattice, the exact solution for the percolation threshold is found to be a hyperbola in thex-p plane, wherex andp are the respective probabilities of each site and bond being unblocked. Percolation threshold for a square and a simple cubic lattice is obtained by computer simulation. We also present a result obtained by a real-space renormalization group technique for the square lattice.     

Magnetic Properties of Transverse Ising Model under a Time Oscillating Longitudinal Field

A transverse Ising spin system, in the presence of time-dependentlongitudinal field, is studied by the effective-field theory (EFT). Theeffective-field equations of motion of the average magnetization are givenfor the simple cubic lattice (Z = 6) and the honeycomb lattice (Z = 3).The Liapunov exponent λ is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. Thedynamic phase transition diagrams in h₀/ ZJ -Γ/ZJ plane and in h₀/ZJ-T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.     

Vortex lattice structural transitions: a Ginzburg-Landau model approach

We analyze the rhombic to square vortex lattice phase transition in anisotropic superconductors using a variant of Ginzburg-Landau theory. The mean-field phase diagram is determined to second order in the anisotropy parameter, and shows a reorientation transition of the square vortex lattice with respect to the crystal lattice. We then derive the long-wavelength elastic moduli of the lattices, and use them to show that thermal fluctuations produce a reentrant rhombic to square lattice transition line, similar to recent studies which used a nonlocal London model.     

Heavy fermions in high magnetic fields

A qualitative picture of the metamagnetic transition in the Anderson lattice model of heavy fermion Ce compounds is described and a strong coupling spin fluctuation theory of the high field state is presented. The field dependence of the minority spin quasiparticle mass is calculated and the onset of the metamagnetic transition with decreasing field is discussed. The theory of the high field state is extended to include Landau levels and the oscillatory behaviour of the spin self-energy as a function of the inverse applied field is investigated. For the heavy fermion model considered such oscillations of the self-energy lead to significant modifications in the standard theory of the de Haas - van Alphen effect. The possible relevance to anomalous experimental results on CeRu₂Si₂ is discussed.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.