35 research outputs found
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 -dimensional soft-self-avoiding
random surfaces on a -dimensional cubic lattice. The energy of a surface
configuration is given by , where is the number of
edges, where two plaquettes meet at a right angle and is the number of
edges, where 4 plaquettes meet. This model can be represented as a
-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 . A low temperature expansion of the
free energy in 3 dimensions up to order () shows,
that for only the ferromagnetic low temperature phases remain stable. An
analysis of low temperature expansions up to order 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 ( and , 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 and a pseudo-gap opens in the
single-particle spectral function for higher values of . The -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 LaSrMnO.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 . 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 there are different
charged particles with spin running from up to , and the
degeneracy is equal to . 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 () properties across the transition temperature, . In order to calculate dependence of physical quantities such as the
spin susceptibility and the electrical resistivity, both above and below
, 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- is determined by quantum Monte Carlo simulations. The
results show that the spin susceptibility does not show a steep singularity at
, 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 , below which a characteristic 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