665 research outputs found
Stochastic Quantization vs. KdV Flows in 2D Quantum Gravity
We consider the stochastic quantization scheme for a non-perturbative
stabilization of 2D quantum gravity and prove that it does not satisfy the KdV
flow equations. It therefore differs from a recently suggested matrix model
which allows real solutions to the KdV equations. The behaviour of the Fermi
energy, the free energy and macroscopic loops in the stochastic quantization
scheme are elucidated.Comment: 17 page
Conference Discussion of the Nuclear Force
Discussion of the nuclear force, lead by a round table consisting of T.
Cohen, E. Epelbaum, R. Machleidt, and F. Gross (chair). After an invited talk
by Machleidt, published elsewhere in these proceedings, brief remarks are made
by Epelbaum, Cohen, and Gross, followed by discussion from the floor moderated
by the chair. The chair asked the round table and the participants to focus on
the following issues: (i) What does each approach (chiral effective field
theory, large Nc, and relativistic phenomenology) contribute to our knowledge
of the nuclear force? Do we need them all? Is any one transcendent? (ii) How
important for applications (few body, nuclear structure, EMC effect, for
example) are precise fits to the NN data below 350 MeV? How precise do these
fits have to be? (iii) Can we learn anything about nonperturbative QCD from
these studies of the nuclear force? The discussion presented here is based on a
video recording made at the conference and transcribed afterward.Comment: Discussion at the 21st European Conference on Few Body Problems
(EFP21) held at Salamanca, Spain, 30 Aug - 3 Sept 201
Self- generated disorder and structural glass formation in homopolymer globules
We have investigated the interrelation between the spin glasses and the
structural glasses. Spin glasses in this case are random magnets without
reflection symmetry (e.g. - spin interaction spin glasses and Potts
glasses) which contain quenched disorder, whereas the structural glasses are
here exemplified by the homopolymeric globule, which can be viewed as a liquid
of connected molecules on nano scales. It is argued that the homopolymeric
globule problem can be mapped onto a disorder field theoretical model whose
effective Hamiltonian resembles the corresponding one for the spin glass model.
In this sense the disorder in the globule is self - generated (in contrast to
spin glasses) and can be related with competitive interactions (virial
coefficients of different signs) and the chain connectivity. The work is aimed
at giving a quantitative description of this analogy. We have investigated the
phase diagram of the homopolymeric globule where the transition line from the
liquid to glassy globule is treated in terms of the replica symmetry breaking
paradigm. The configurational entropy temperature dependence is also discussed.Comment: 22 pages, 4 figures, submitted to Phys. Rev.
Finite dimensional corrections to mean field in a short-range p-spin glassy model
In this work we discuss a short range version of the -spin model. The
model is provided with a parameter that allows to control the crossover with
the mean field behaviour. We detect a discrepancy between the perturbative
approach and numerical simulation. We attribute it to non-perturbative effects
due to the finite probability that each particular realization of the disorder
allows for the formation of regions where the system is less frustrated and
locally freezes at a higher temperature.Comment: 18 pages, 5 figures, submitted to Phys Rev
Simplest random K-satisfiability problem
We study a simple and exactly solvable model for the generation of random
satisfiability problems. These consist of random boolean constraints
which are to be satisfied simultaneously by logical variables. In
statistical-mechanics language, the considered model can be seen as a diluted
p-spin model at zero temperature. While such problems become extraordinarily
hard to solve by local search methods in a large region of the parameter space,
still at least one solution may be superimposed by construction. The
statistical properties of the model can be studied exactly by the replica
method and each single instance can be analyzed in polynomial time by a simple
global solution method. The geometrical/topological structures responsible for
dynamic and static phase transitions as well as for the onset of computational
complexity in local search method are thoroughly analyzed. Numerical analysis
on very large samples allows for a precise characterization of the critical
scaling behaviour.Comment: 14 pages, 5 figures, to appear in Phys. Rev. E (Feb 2001). v2: minor
errors and references correcte
The nature of slow dynamics in a minimal model of frustration-limited domains
We present simulation results for the dynamics of a schematic model based on
the frustration-limited domain picture of glass-forming liquids. These results
are compared with approximate theoretical predictions analogous to those
commonly used for supercooled liquid dynamics. Although model relaxation times
increase by several orders of magnitude in a non-Arrhenius manner as a
microphase separation transition is approached, the slow relaxation is in many
ways dissimilar to that of a liquid. In particular, structural relaxation is
nearly exponential in time at each wave vector, indicating that the mode
coupling effects dominating liquid relaxation are comparatively weak within
this model. Relaxation properties of the model are instead well reproduced by
the simplest dynamical extension of a static Hartree approximation. This
approach is qualitatively accurate even for temperatures at which the mode
coupling approximation predicts loss of ergodicity. These results suggest that
the thermodynamically disordered phase of such a minimal model poorly
caricatures the slow dynamics of a liquid near its glass transition
Threshold Corrections and Gauge Symmetry in Twisted Superstring Models
Threshold corrections to the running of gauge couplings are calculated for
superstring models with free complex world sheet fermions. For two N=1
models, the threshold corrections lead to a small increase
in the unification scale. Examples are given to illustrate how a given particle
spectrum can be described by models with different boundary conditions on the
internal fermions. We also discuss how complex twisted fermions can enhance the
symmetry group of an N=4 model to the gauge group
. It is then shown how a mixing angle analogous
to the Weinberg angle depends on the boundary conditions of the internal
fermions.Comment: easier to Tex version, figures to be sent separatel
Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems
Type I - heterotic duality in D=10 predicts various relations and constraints
on higher order F^n couplings at different string loop levels on both sides. We
prove the vanishing of two-loop corrections to the heterotic F^4 terms, which
is one of the basic predictions from this duality. Furthermore, we show that
the heterotic F^5 and (CP even) F^6 couplings are not renormalized at one loop.
These results strengthen the conjecture that in D=10 any Tr F^(2n) coupling
appears only at the disc tree-level on type I side and at (n-1)-loop level on
the heterotic side. Our non-renormalization theorems are valid in any heterotic
string vacuum with sixteen supercharges.Comment: 35 pages, harvmac; cosmetic changes; final version to appear in NP
Dynamics of Phase Transitions by Hysteresis Methods I
In studies of the QCD deconfining phase transition or crossover by means of
heavy ion experiments, one ought to be concerned about non-equilibrium effects
due to heating and cooling of the system. Motivated by this, we look at
hysteresis methods to study the dynamics of phase transitions. Our systems are
temperature driven through the phase transition using updating procedures in
the Glauber universality class. Hysteresis calculations are presented for a
number of observables, including the (internal) energy, properties of
Fortuin-Kasteleyn clusters and structure functions. We test the methods for 2d
Potts models, which provide a rich collection of phase transitions with a
number of rigorously known properties. Comparing with equilibrium
configurations we find a scenario where the dynamics of the transition leads to
a spinodal decomposition which dominates the statistical properties of the
configurations. One may expect an enhancement of low energy gluon production
due to spinodal decomposition of the Polyakov loops, if such a scenario is
realized by nature.Comment: 12 pages, revised after referee report, to appear in Phys. Rev.
Aging without disorder on long time scales
We study the Metropolis dynamics of a simple spin system without disorder,
which exhibits glassy dynamics at low temperatures. We use an implementation of
the algorithm of Bortz, Kalos and Lebowitz \cite{bortz}. This method turns out
to be very efficient for the study of glassy systems, which get trapped in
local minima on many different time scales. We find strong evidence of aging
effects at low temperatures. We relate these effects to the distribution
function of the trapping times of single configurations.Comment: 8 pages Revtex, 7 figures uuencoded (Revised version: the figures are
now present
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