Phase Transition in Lattice Surface Systems with Gonihedric Action

We prove the existence of an ordered low temperature phase in a model of soft-self-avoiding closed random surfaces on a cubic lattice by a suitable extension of Peierls contour method. The statistical weight of each surface configuration depends only on the mean extrinsic curvature and on an interaction term arising when two surfaces touch each other along some contour. The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version of the gonihedric string, which is an action for triangulated random surfaces.Comment: 17 pages, Postscript figures include

Low temperature expansion of the gonihedric Ising model

We investigate a model of closed $(d-1)$-dimensional soft-self-avoiding random surfaces on a $d$-dimensional cubic lattice. The energy of a surface configuration is given by $E=J(n_{2}+4k n_{4})$, where $n_{2}$ is the number of edges, where two plaquettes meet at a right angle and $n_{4}$ is the number of edges, where 4 plaquettes meet. This model can be represented as a $\Z_{2}$-spin system with ferromagnetic nearest-neighbour-, antiferromagnetic next-nearest-neighbour- and plaquette-interaction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaption of Peierls argument, we prove the existence of infinitely many ordered low temperature phases for the case $k=0$. A low temperature expansion of the free energy in 3 dimensions up to order $x^{38}$ ($x={e}^{-\beta J}$) shows, that for $k>0$ only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order $x^{44}$ for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results.Comment: 27 pages, Postscript figures include

Reentrant charge order transition in the extended Hubbard model

We study the extended Hubbard model with both on-site and nearest neighbor Coulomb repulsion ($U$ and $V$, respectively) in the Dynamical Mean Field theory. At quarter filling, the model shows a transition to a charge ordered phase with different sublattice occupancies n_A \nen_B. The effective mass increases drastically at the critical $V$ and a pseudo-gap opens in the single-particle spectral function for higher values of $V$. The $V_c(T)$-curve has a negative slope for small temperatures, i.e. the charge ordering transition can be driven by increasing the temperature. This is due to the higher spin-entropy of the charge ordered phase.Comment: 4 pages, 4 EPS figures included, REVTe

Charge-order transition in the extended Hubbard model on a two-leg ladder

We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion V using the Density Matrix Renormalization Group technique. We consider electron densities between quarter and half filling. For quarter filling and U=8t, we find evidence for a continuous phase transition between a homogeneous state at small V and a broken-symmetry state with "checkerboard" [wavevector Q=(pi,pi)] charge order at large V. This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of U/t on the transition and estimate the position of the tricritical points.Comment: 4 pages, 5 figs, minor changes, accepted for publication in PRB R

The Numerical Renormalization Group Method for correlated electrons

The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular the results for the Mott metal-insulator transition at low temperatures.Comment: 14 pages, 7 eps-figures include

Reentrant charge ordering caused by polaron formation

Based on a two-dimensional extended Hubbard model with electron-phonon interaction, we have studied the effect of polaron formation on the charge ordering (CO) transition. It is found that for fully ferromagnetically ordered spins the CO state may go through a process of appearance, collapse and reappearance with decreasing temperature. This is entirely due to a emperature-dependent polaron bandwidth. On the other hand, when a paramagnetic spin state is considered, only a simple reentrant behavior of the CO transition is found, which is only partly due to polaron effect. This model is proposed as an explanation of the observed reentrant behavior of the CO transition in the layered manganite LaSr$_2$Mn$_2$O$_7$.Comment: 4 pages, 2 eps figures, revised version accepted by Phys. Rev. Let

The QCD string and the generalised wave equation

The equation for QCD string proposed earlier is reviewed. This equation appears when we examine the gonihedric string model and the corresponding transfer matrix. Arguing that string equation should have a generalized Dirac form we found the corresponding infinite-dimensional gamma matrices as a symmetric solution of the Majorana commutation relations. The generalized gamma matrices are anticommuting and guarantee unitarity of the theory at all orders of $v/c$. In the second quantized form the equation does not have unwanted ghost states in Fock space. In the absence of Casimir mass terms the spectrum reminds hydrogen exitations. On every mass level $r=2,4,..$ there are different charged particles with spin running from $j=1/2$ up to $j_{max}=r-1/2$, and the degeneracy is equal to $d_{r}=2r-1 = 2j_{max}$. This is in contrast with the exponential degeneracy in superstring theory.Comment: 11 pages LaTeX, uses lamuphys.sty and bibnorm.sty,; Based on talks given at the 6th Hellenic School and Workshop on Elementary Particle Physics, Corfu, Greece, September 19-26, 1998 and at the International Workshop "ISMP", Tbilisi, Georgia, September 12-18, 199

Finite temperature numerical renormalization group study of the Mott-transition

Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for T<T_c approx 0.02W (W: bandwidth) we find hysteresis with first-order transitions both at U_c1 (defining the insulator to metal transition) and at U_c2 (defining the metal to insulator transition), at T>T_c there is a smooth crossover from metallic-like to insulating-like solutions.Comment: 10 pages, 9 eps-figure

Phase diagram of the quarter-filled extended Hubbard model on a two-leg ladder

We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion V using the Density Matrix Renormalization Group technique. The ground-state is homogeneous at small V, a ``checkerboard'' charge--ordered insulator at large V and not too small on-site Coulomb repulsion U, and is phase-separated for moderate or large V and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper, we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling charge-ordered regime which maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.Comment: 12 pages, 13 figures, submitted to PRB, presentation revised, new results added (metallic phase at small U and V

Finite-Temperature Properties across the Charge Ordering Transition -- Combined Bosonization, Renormalization Group, and Numerical Methods

We theoretically describe the charge ordering (CO) metal-insulator transition based on a quasi-one-dimensional extended Hubbard model, and investigate the finite temperature ($T$) properties across the transition temperature, $T_{\rm CO}$. In order to calculate $T$ dependence of physical quantities such as the spin susceptibility and the electrical resistivity, both above and below $T_{\rm CO}$, a theoretical scheme is developed which combines analytical methods with numerical calculations. We take advantage of the renormalization group equations derived from the effective bosonized Hamiltonian, where Lanczos exact diagonalization data are chosen as initial parameters, while the CO order parameter at finite-$T$ is determined by quantum Monte Carlo simulations. The results show that the spin susceptibility does not show a steep singularity at $T_{\rm CO}$, and it slightly increases compared to the case without CO because of the suppression of the spin velocity. In contrast, the resistivity exhibits a sudden increase at $T_{\rm CO}$, below which a characteristic $T$ dependence is observed. We also compare our results with experiments on molecular conductors as well as transition metal oxides showing CO.Comment: 9 pages, 8 figure