69 research outputs found
Triviality Bounds in Two-Doublet Models
We examine perturbatively the two-Higgs-doublet extension of the \SM\ in the
context of the suspected triviality of theories with fundamental scalars.
Requiring the model to define a consistent effective theory for scales below a
cutoff of times the largest mass of the problem, as motivated by lattice
investigations of the one-Higgs-doublet model, we obtain combined bounds for
the parameters of the model. We find upper limits of 470 GeV for the mass of
the light --even neutral scalar and 650--700 GeV for the other scalar
masses.Comment: 15 pages (8 postscript figures in two files), BUHEP-93-
A Numerical Study of Phase Transitions Inside the Pores of Aerogels
Phase transitions inside the pores of an aerogel are investigated by
modelizing the aerogel structure by diffusion-limited cluster-cluster
aggregation on a cubic lattice in a finite box and considering -states Potts
variables on the empty sites interacting via nearest-neighbours. Using a finite
size scaling analysing of Monte-Carlo numerical results, it is concluded that
for the transition changes from first order to second order as the
aerogel concentration (density) increases. Comparison is made with the case
(where the first order transition is weaker in three dimensions) and with
the case but for randomly (non correlated) occupied sites. Possible
applications to experiments are discussed.Comment: RevTex, 12 pages + 10 postscript figures compressed using "uufiles",
To appear in J. of Non-Cryst. Solid
Continuous Versus First Order Transitions in Compressible Diluted Magnets
The interplay between disorder and compressibility in Ising magnets is
studied. Contrary to pure systems in which a weak compressibility drives the
transition first order, we find from a renormalization group analysis that it
has no effect on disordered systems which keep undergoing continuous transition
with rigid random-bond Ising model critical exponents. The mean field
calculation exhibits a dilution-dependent tricritical point beyond which, at
stronger compressibility the transition is first order. The different behavior
of XY and Heisenberg magnets is discussed.Comment: 16 pages, latex, 2 figures not include
Phase Transition in the Two Dimensional Classical XY Model
For the two dimensional classical XY model we present extensive high
-temperature -phase bulk data extracted based on a novel finite size scaling
(FSS) Monte Carlo technique, along with FSS data near criticality. Our data
verify that sets in near criticality, and clarify the nature of
correction to the leading scaling behavior. However, the result of standard FSS
analysis near criticality is inconsistent with other predictions of
Kosterlitz's renormalization group approach.Comment: Significant changes in the text and the figures. To appear in Phys.
Lett. A Hard copies of seven figures are available upon reques
Relaxation times of kinetically constrained spin models with glassy dynamics
We analyze the density and size dependence of the relaxation time for
kinetically constrained spin systems. These have been proposed as models for
strong or fragile glasses and for systems undergoing jamming transitions. For
the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any
density and for the Knight model below the critical density at which
the glass transition occurs, we show that the persistence and the spin-spin
time auto-correlation functions decay exponentially. This excludes the
stretched exponential relaxation which was derived by numerical simulations.
For FA2f in , we also prove a super-Arrhenius scaling of the form
. For FA1f in = we
rigorously prove the power law scalings recently derived in \cite{JMS} while in
we obtain upper and lower bounds consistent with findings therein.
Our results are based on a novel multi-scale approach which allows to analyze
in presence of kinetic constraints and to connect time-scales and
dynamical heterogeneities. The techniques are flexible enough to allow a
variety of constraints and can also be applied to conservative stochastic
lattice gases in presence of kinetic constraints.Comment: 4 page
Renormalization Theory for Interacting Crumpled Manifolds
We consider a continuous model of D-dimensional elastic (polymerized)
manifold fluctuating in d-dimensional Euclidean space, interacting with a
single impurity via an attractive or repulsive delta-potential (but without
self-avoidance interactions). Except for D=1 (the polymer case), this model
cannot be mapped onto a local field theory. We show that the use of intrinsic
distance geometry allows for a rigorous construction of the high-temperature
perturbative expansion and for analytic continuation in the manifold dimension
D. We study the renormalization properties of the model for 0<D<2, and show
that for d<d* where d*=2D/(2-D) is the upper critical dimension, the
perturbative expansion is UV finite, while UV divergences occur as poles at
d=d*. The standard proof of perturbative renormalizability for local field
theories (the BPH theorem) does not apply to this model. We prove perturbative
renormalizability to all orders by constructing a subtraction operator based on
a generalization of the Zimmermann forests formalism, and which makes the
theory finite at d=d*. This subtraction operation corresponds to a
renormalization of the coupling constant of the model (strength of the
interaction with the impurity). The existence of a Wilson function, of an
epsilon-expansion around the critical dimension, of scaling laws for d<d* in
the repulsive case, and of non-trivial critical exponents of the delocalization
transition for d>d* in the attractive case is thus established. To our
knowledge, this provides the first proof of renormalizability for a model of
extended objects, and should be applicable to the study of self-avoidance
interactions for random manifolds.Comment: 126 pages (+ 24 figures not included available upon request),
harvmac, SPhT/92/12
Phase diagram of the ABC model on an interval
The three species asymmetric ABC model was initially defined on a ring by
Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was
later studied by Clincy, Derrida, and Evans. Here the latter model is studied
on a one-dimensional lattice of N sites with closed (zero flux) boundaries. In
this geometry the local particle conserving dynamics satisfies detailed balance
with respect to a canonical Gibbs measure with long range asymmetric pair
interactions. This generalizes results for the ring case, where detailed
balance holds, and in fact the steady state measure is known only for the case
of equal densities of the different species: in the latter case the stationary
states of the system on a ring and on an interval are the same. We prove that
in the N to infinity limit the scaled density profiles are given by (pieces of)
the periodic trajectory of a particle moving in a quartic confining potential.
We further prove uniqueness of the profiles, i.e., the existence of a single
phase, in all regions of the parameter space (of average densities and
temperature) except at low temperature with all densities equal; in this case a
continuum of phases, differing by translation, coexist. The results for the
equal density case apply also to the system on the ring, and there extend
results of Clincy et al.Comment: 52 pages, AMS-LaTeX, 8 figures from 10 eps figure files. Revision:
minor changes in response to referee reports; paper to appear in J. Stat.
Phy
Inhomogeneity-induced second-order phase transitions in Potts model on hierarchical lattices
The thermodynamics of the -state Potts model with arbitrary on a class
of hierarchical lattices is considered. Contrary to the case of the crystal
lattices, it has always the second-order phase transitions. The analytical
expressions fo the critical indexes are obtained, their dependencies on the
structural lattice pararmeters are studied and the scailing relations among
them are establised. The structural criterion of the inhomogeneity-induced
transformation of the transition order is suggested. The application of the
results to a description of critical phenomena in the dilute crystals and
substances confined in porous media is discussed.Comment: 9 pages, 2 figure
Interpolating the Stage of Exponential Expansion in the Early Universe: a possible alternative with no reheating
In the standard picture, the inflationary universe is in a supercooled state
which ends with a short time, large scale reheating period, after which the
universe goes into a radiation dominated stage. An alternative is proposed here
in which the radiation energy density smoothly decreases all during an
inflation-like stage and with no discontinuity enters the subsequent radiation
dominated stage. The scale factor is calculated from standard Friedmann
cosmology in the presence of both radiation and vacuum energy density. A large
class of solutions confirm the above identified regime of non-reheating
inflation-like behavior for observationally consistent expansion factors and
not too large a drop in the radiation energy density. One dynamical realization
of such inflation without reheating is from warm inflation type scenarios.
However the solutions found here are properties of the Einstein equations with
generality beyond slow-roll inflation scenarios. The solutions also can be
continuously interpolated from the non-reheating type behavior to the standard
supercooled limit of exponential expansion, thus giving all intermediate
inflation-like behavior between these two extremes. The temperature of the
universe and the expansion factor are calculated for various cases.
Implications for baryongenesis are discussed. This non-reheating,
inflation-like regime also appears to have some natural features for a universe
that is between nearly flat and open.Comment: 26 pages, Latex, 2 figures, In press Physical Review
Jamming percolation and glassy dynamics
We present a detailed physical analysis of the dynamical glass-jamming
transition which occurs for the so called Knight models recently introduced and
analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we
review some of our previous works on Kinetically Constrained Models.
The Knights models correspond to a new class of kinetically constrained
models which provide the first example of finite dimensional models with an
ideal glass-jamming transition. This is due to the underlying percolation
transition of particles which are mutually blocked by the constraints. This
jamming percolation has unconventional features: it is discontinuous (i.e. the
percolating cluster is compact at the transition) and the typical size of the
clusters diverges faster than any power law when . These
properties give rise for Knight models to an ergodicity breaking transition at
: at and above a finite fraction of the system is frozen. In
turn, this finite jump in the density of frozen sites leads to a two step
relaxation for dynamic correlations in the unjammed phase, analogous to that of
glass forming liquids. Also, due to the faster than power law divergence of the
dynamical correlation length, relaxation times diverge in a way similar to the
Vogel-Fulcher law.Comment: Submitted to the special issue of Journal of Statistical Physics on
Spin glasses and related topic
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