65 research outputs found
The superconducting phase transition and gauge dependence
The gauge dependence of the renormalization group functions of the
Ginzburg-Landau model is investigated. The analysis is done by means of the
Ward-Takahashi identities. After defining the local superconducting order
parameter, it is shown that its exponent is in fact gauge independent.
This happens because in the Landau gauge is the only gauge having a
physical meaning, a property not shared by the four-dimensional model where any
gauge choice is possible. The analysis is done in both the context of the
-expansion and in the fixed dimension approach. It is pointed out the
differences that arise in both of these approaches concerning the gauge
dependence.Comment: RevTex, 3 pages, no figures; accepted for publication in PRB; this
paper is a short version of cond-mat/990527
Multiplicative processes and power laws
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of
stochastic processes with multiplicative noise, which have been studied in
several different contexts over the past decades. We focus on the regime, found
for a generic set of control parameters, in which stochastic processes with
multiplicative noise produce intermittency of a special kind, characterized by
a power law probability density distribution. We briefly explain the physical
mechanism leading to a power law pdf and provide a list of references for these
results dating back from a quarter of century. We explain how the formulation
in terms of the characteristic function developed by Takayasu et al. can be
extended to exponents , which explains the ``reason of the lucky
coincidence''. The multidimensional generalization of (\ref{eq1}) and the
available results are briefly summarized. The discovery of stretched
exponential tails in the presence of the cut-off introduced in \cite{Taka} is
explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998
Improved radiative corrections for (e,e'p) experiments: Beyond the peaking approximation and implications of the soft-photon approximation
Analysing (e,e'p) experimental data involves corrections for radiative
effects which change the interaction kinematics and which have to be carefully
considered in order to obtain the desired accuracy. Missing momentum and energy
due to bremsstrahlung have so far always been calculated using the peaking
approximation which assumes that all bremsstrahlung is emitted in the direction
of the radiating particle. In this article we introduce a full angular Monte
Carlo simulation method which overcomes this approximation. The angular
distribution of the bremsstrahlung photons is reconstructed from H(e,e'p) data.
Its width is found to be underestimated by the peaking approximation and
described much better by the approach developed in this work.Comment: 11 pages, 13 figure
Random wetting transition on the Cayley tree : a disordered first-order transition with two correlation length exponents
We consider the random wetting transition on the Cayley tree, i.e. the
problem of a directed polymer on the Cayley tree in the presence of random
energies along the left-most bonds. In the pure case, there exists a
first-order transition between a localized phase and a delocalized phase, with
a correlation length exponent . In the disordered case, we find
that the transition remains first-order, but that there exists two diverging
length scales in the critical region : the typical correlation length diverges
with the exponent , whereas the averaged correlation length
diverges with the bigger exponent and governs the finite-size
scaling properties. We describe the relations with previously studied models
that are governed by the same "Infinite Disorder Fixed Point". For the present
model, where the order parameter is the contact density
(defined as the ratio of the number of contacts over the total length
), the notion of "infinite disorder fixed point" means that the thermal
fluctuations of within a given sample, become negligeable at large
scale with respect to sample-to-sample fluctuations. We characterize the
statistics over the samples of the free-energy and of the contact density. In
particular, exactly at criticality, we obtain that the contact density is not
self-averaging but remains distributed over the samples in the thermodynamic
limit, with the distribution .Comment: 15 pages, 1 figur
A record-driven growth process
We introduce a novel stochastic growth process, the record-driven growth
process, which originates from the analysis of a class of growing networks in a
universal limiting regime. Nodes are added one by one to a network, each node
possessing a quality. The new incoming node connects to the preexisting node
with best quality, that is, with record value for the quality. The emergent
structure is that of a growing network, where groups are formed around record
nodes (nodes endowed with the best intrinsic qualities). Special emphasis is
put on the statistics of leaders (nodes whose degrees are the largest). The
asymptotic probability for a node to be a leader is equal to the Golomb-Dickman
constant omega=0.624329... which arises in problems of combinatorical nature.
This outcome solves the problem of the determination of the record breaking
rate for the sequence of correlated inter-record intervals. The process
exhibits temporal self-similarity in the late-time regime. Connections with the
statistics of the cycles of random permutations, the statistical properties of
randomly broken intervals, and the Kesten variable are given.Comment: 30 pages,5 figures. Minor update
From Rational Bubbles to Crashes
We study and generalize in various ways the model of rational expectation
(RE) bubbles introduced by Blanchard and Watson in the economic literature.
First, bubbles are argued to be the equivalent of Goldstone modes of the
fundamental rational pricing equation, associated with the symmetry-breaking
introduced by non-vanishing dividends. Generalizing bubbles in terms of
multiplicative stochastic maps, we summarize the result of Lux and Sornette
that the no-arbitrage condition imposes that the tail of the return
distribution is hyperbolic with an exponent mu<1. We then extend the RE bubble
model to arbitrary dimensions d and, with the renewal theory for products of
random matrices applied to stochastic recurrence equations, we extend the
theorem of Lux and Sornette to demonstrate that the tails of the unconditional
distributions follow power laws, with the same asymptotic tail exponent mu<1
for all assets. Two extensions (the crash hazard rate model and the
non-stationary growth rate model) of the RE bubble model provide ways of
reconciliation with the stylized facts of financial data. The later model
allows for an understanding of the breakdown of the fundamental valuation
formula as deeply associated with a spontaneous breaking of the price symmetry.
Its implementation for multi-dimensional bubbles explains why the tail index mu
seems to be the same for any group af assets as observed empirically. This work
begs for the introduction of a generalized field theory which would be able to
capture the spontaneous breaking of symmetry, recover the fundamental valuation
formula in the normal economic case and extend it to the still unexplored
regime where the economic growth rate is larger than the discount growth rate.Comment: Latex 27 pages with 3 eps figur
Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization
The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study
singular quantities in the Griffiths phase of random quantum spin chains. For
the random transverse-field Ising spin chain we have extended Fisher's
analytical solution to the off-critical region and calculated the dynamical
exponent exactly. Concerning other random chains we argue by scaling
considerations that the RG method generally becomes asymptotically exact for
large times, both at the critical point and in the whole Griffiths phase. This
statement is checked via numerical calculations on the random Heisenberg and
quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include
Even-visiting random walks: exact and asymptotic results in one dimension
We reconsider the problem of even-visiting random walks in one dimension.
This problem is mapped onto a non-Hermitian Anderson model with binary
disorder. We develop very efficient numerical tools to enumerate and
characterize even-visiting walks. The number of closed walks is obtained as an
exact integer up to 1828 steps, i.e., some walks. On the analytical
side, the concepts and techniques of one-dimensional disordered systems allow
to obtain explicit asymptotic estimates for the number of closed walks of
steps up to an absolute prefactor of order unity, which is determined
numerically. All the cumulants of the maximum height reached by such walks are
shown to grow as , with exactly known prefactors. These results
illustrate the tight relationship between even-visiting walks, trapping models,
and the Lifshitz tails of disordered electron or phonon spectra.Comment: 24 pages, 4 figures. To appear in J. Phys.
Critical properties of the topological Ginzburg-Landau model
We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons
term added. The flow diagram contains two charged fixed points corresponding to
the tricritical and infrared stable fixed points. The topological coupling
controls the fixed point structure and eventually the region of first order
transitions disappears. We compute the critical exponents as a function of the
topological coupling. We obtain that the value of the exponent does not
vary very much from the XY value, . This shows that the
Chern-Simons term does not affect considerably the XY scaling of
superconductors. We discuss briefly the possible phenomenological applications
of this model.Comment: RevTex, 7 pages, 8 figure
Phase Structure of d=2+1 Compact Lattice Gauge Theories and the Transition from Mott Insulator to Fractionalized Insulator
Large-scale Monte Carlo simulations are employed to study phase transitions
in the three-dimensional compact abelian Higgs model in adjoint representations
of the matter field, labelled by an integer q, for q=2,3,4,5. We also study
various limiting cases of the model, such as the lattice gauge theory,
dual to the spin model, and the 3DXY spin model which is dual to the
lattice gauge theory in the limit . We have computed the
first, second, and third moments of the action to locate the phase transition
of the model in the parameter space , where is the
coupling constant of the matter term, and is the coupling constant of
the gauge term. We have found that for q=3, the three-dimensional compact
abelian Higgs model has a phase-transition line which
is first order for below a finite {\it tricritical} value
, and second order above. We have found that the
first order phase transition persists for finite and
joins the second order phase transition at a tricritical point
. For
all other integer we have considered, the entire phase transition
line is critical.Comment: 17 pages, 12 figures (new Fig. 2), new Section IVB, updated
references, submitted to Physical Review
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