The Phase Diagram of the Gonihedric 3d Ising Model via CVM

We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string worldsheets of the gonihedric string embedded in ${\bf Z}^3$. The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a result the action depends only on the angles of the discrete surface and not on the area, which is the antithesis of the standard 3d Ising model. The results obtained with the CVM are in good agreement with Monte Carlo simulations for the critical temperatures and the order of the transition as the self-avoidance coupling $\kappa$ is varied. The value of the magnetization critical exponent $\beta = 0.062 \pm 0.003$, calculated with the cluster variation--Pad\`e approximant method, is also close to the simulation results.Comment: 8 pages text (LaTex) + 3 eps figures bundled together with uufile

Three-dimensional Gonihedric Potts model

We study, by the Mean Field and Monte Carlo methods, a generalized q-state Potts gonihedric model. The phase transition of the model becomes stronger with increasing $q.$ The value $k_c(q),$ at which the phase transition becomes second order, turns out to be an increasing function of $q.$Comment: 11 pages, 7 figure

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

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

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 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

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

Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type

We consider the electronic properties of layered molecular crystals of the type theta-D$_2$A, where A is an anion and D is a donor molecule such as BEDT-TTF [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] which is arranged in the theta type pattern within the layers. We argue that the simplest strongly correlated electron model that can describe the rich phase diagram of these materials is the extended Hubbard model on the square lattice at a quarter filling. In the limit where the Coulomb repulsion on a single site is large, the nearest-neighbour Coulomb repulsion, V, plays a crucial role. When V is much larger than the intermolecular hopping integral t the ground state is an insulator with charge ordering. In this phase antiferromagnetism arises due to a novel fourth-order superexchange process around a plaquette on the square lattice. We argue that the charge ordered phase is destroyed below a critical non-zero value V, of the order of t. Slave boson theory is used to explicitly demonstrate this for the SU(N) generalisation of the model, in the large N limit. We also discuss the relevance of the model to the all-organic family beta''-(BEDT-TTF)$_2$SF$_5$YSO$_3$ where Y = CH$_2$CF$_2$, CH$_2$, CHF.Comment: 15 pages, 6 eps figure