240 research outputs found
Extended scaling relations for planar lattice models
It is widely believed that the critical properties of several planar lattice
models, like the Eight Vertex or the Ashkin-Teller models, are well described
by an effective Quantum Field Theory obtained as formal scaling limit. On the
basis of this assumption several extended scaling relations among their indices
were conjectured. We prove the validity of some of them, among which the ones
by Kadanoff, [K], and by Luther and Peschel, [LP].Comment: 32 pages, 7 fi
On Duality of Two-dimensional Ising Model on Finite Lattice
It is shown that the partition function of the 2d Ising model on the dual
finite lattice with periodical boundary conditions is expressed through some
specific combination of the partition functions of the model on the torus with
corresponding boundary conditions. The generalization of the duality relations
for the nonhomogeneous case is given. These relations are proved for the
weakly-nonhomogeneous distribution of the coupling constants for the finite
lattice of arbitrary sizes. Using the duality relations for the nonhomogeneous
Ising model, we obtain the duality relations for the two-point correlation
function on the torus, the 2d Ising model with magnetic fields applied to the
boundaries and the 2d Ising model with free, fixed and mixed boundary
conditions.Comment: 18 pages, LaTe
Twistfield Perturbations of Vertex Operators in the Z_2-Orbifold Model
We apply Kadanoff's theory of marginal deformations of conformal field
theories to twistfield deformations of Z_2 orbifold models in K3 moduli space.
These deformations lead away from the Z_2 orbifold sub-moduli-space and hence
help to explore conformal field theories which have not yet been understood. In
particular, we calculate the deformation of the conformal dimensions of vertex
operators for p^2<1 in second order perturbation theory.Comment: Latex2e, 19 pages, 1 figur
The Hydrodynamics of M-Theory
We consider the low energy limit of a stack of N M-branes at finite
temperature. In this limit, the M-branes are well described, via the AdS/CFT
correspondence, in terms of classical solutions to the eleven dimensional
supergravity equations of motion. We calculate Minkowski space two-point
functions on these M-branes in the long-distance, low-frequency limit, i.e. the
hydrodynamic limit, using the prescription of Son and Starinets
[hep-th/0205051]. From these Green's functions for the R-currents and for
components of the stress-energy tensor, we extract two kinds of diffusion
constant and a viscosity. The N dependence of these physical quantities may
help lead to a better understanding of M-branes.Comment: 1+19 pages, references added, section 5 clarified, eq. (72) correcte
Word Processors with Line-Wrap: Cascading, Self-Organized Criticality, Random Walks, Diffusion, Predictability
We examine the line-wrap feature of text processors and show that adding
characters to previously formatted lines leads to the cascading of words to
subsequent lines and forms a state of self-organized criticality. We show the
connection to one-dimensional random walks and diffusion problems, and we
examine the predictability of catastrophic cascades.Comment: 6 pages, LaTeX with RevTeX package, 4 postscript figures appende
On explicit results at the intersection of the Z_2 and Z_4 orbifold subvarieties in K3 moduli space
We examine the recently found point of intersection between the Z_2 and Z_4
orbifold subvarieties in the K3 moduli space more closely. First we give an
explicit identification of the coordinates of the respective Z_2 and Z_4
orbifold theories at this point. Secondly we construct the explicit
identification of conformal field theories at this point and show the
orthogonality of the two subvarieties.Comment: Latex, 23 page
Off-shell effects on particle production
We investigate the observable effects of off-shell propagation of nucleons in
heavy-ion collisions at SIS energies. Within a semi-classical BUU transport
model we find a strong enhancement of subthreshold particle production when
off-shell nucleons are propagated.Comment: 11 pages, 3 figure
Collective edge modes in fractional quantum Hall systems
Over the past few years one of us (Murthy) in collaboration with R. Shankar
has developed an extended Hamiltonian formalism capable of describing the
ground state and low energy excitations in the fractional quantum Hall regime.
The Hamiltonian, expressed in terms of Composite Fermion operators,
incorporates all the nonperturbative features of the fractional Hall regime, so
that conventional many-body approximations such as Hartree-Fock and
time-dependent Hartree-Fock are applicable. We apply this formalism to develop
a microscopic theory of the collective edge modes in fractional quantum Hall
regime. We present the results for edge mode dispersions at principal filling
factors and for systems with unreconstructed edges. The
primary advantage of the method is that one works in the thermodynamic limit
right from the beginning, thus avoiding the finite-size effects which
ultimately limit exact diagonalization studies.Comment: 12 pages, 9 figures, See cond-mat/0303359 for related result
Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems
Modification of the renormalization-group approach, invoking Stratonovich
transformation at each step, is proposed to describe phase transitions in 3D
Ising-class systems. The proposed method is closely related to the mean-field
approximation. The low-order scheme works well for a wide thermal range, is
consistent with a scaling hypothesis and predicts very reasonable values of
critical indices.Comment: 4 page
Diffusive Thermal Dynamics for the Ising Ferromagnet
We introduce a thermal dynamics for the Ising ferromagnet where the energy
variations occurring within the system exhibit a diffusive character typical of
thermalizing agents such as e.g. localized excitations. Time evolution is
provided by a walker hopping across the sites of the underlying lattice
according to local probabilities depending on the usual Boltzmann weight at a
given temperature. Despite the canonical hopping probabilities the walker
drives the system to a stationary state which is not reducible to the canonical
equilibrium state in a trivial way. The system still exhibits a magnetic phase
transition occurring at a finite value of the temperature larger than the
canonical one. The dependence of the model on the density of walkers realizing
the dynamics is also discussed. Interestingly the differences between the
stationary state and the Boltzmann equilibrium state decrease with increasing
number of walkers.Comment: 9 pages, 14 figures. Accepted for publication on PR
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