71 research outputs found
Strings with Extrinsic Curvature: An Analysis of the Crossover Regime
We present the results of a set of Monte Carlo simulations of Dynamically
Triangulated Random Surfaces embedded in three dimensions with an extrinsic
curvature dependent action. We analyze several observables in the crossover
regime and discuss whether or not our observations are indicative of the
presence of a phase transition.Comment: (Contribution to Lattice 92 Proceedings.) Latex file (5 pages),
requires espcrc2.sty. 2 figures not included. Syracuse preprint
SU-HEP-4241-52
The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature
We present the results of a large-scale simulation of a Dynamically
Triangulated Random Surface with extrinsic curvature embedded in
three-dimensional flat space. We measure a variety of local observables and use
a finite size scaling analysis to characterize as much as possible the regime
of crossover from crumpled to smooth surfaces.Comment: 29 pages. There are also 19 figures available from the authors but
not included here - sorr
Universality and its Origins at the Amorphous Solidification Transition
Systems undergoing an equilibrium phase transition from a liquid state to an
amorphous solid state exhibit certain universal characteristics. Chief among
these are the fraction of particles that are randomly localized and the scaling
functions that describe the order parameter and (equivalently) the statistical
distribution of localization lengths for these localized particles. The purpose
of this Paper is to discuss the origins and consequences of this universality,
and in doing so, three themes are explored. First, a replica-Landau-type
approach is formulated for the universality class of systems that are composed
of extended objects connected by permanent random constraints and undergo
amorphous solidification at a critical density of constraints. This formulation
generalizes the cases of randomly cross-linked and end-linked macromolecular
systems, discussed previously. The universal replica free energy is
constructed, in terms of the replica order parameter appropriate to amorphous
solidification, the value of the order parameter is obtained in the liquid and
amorphous solid states, and the chief universal characteristics are determined.
Second, the theory is reformulated in terms of the distribution of local static
density fluctuations rather than the replica order parameter. It is shown that
a suitable free energy can be constructed, depending on the distribution of
static density fluctuations, and that this formulation yields precisely the
same conclusions as the replica approach. Third, the universal predictions of
the theory are compared with the results of extensive numerical simulations of
randomly cross-linked macromolecular systems, due to Barsky and Plischke, and
excellent agreement is found.Comment: 10 pages, including 3 figures (REVTEX
Domain growth and aging scaling in coarsening disordered systems
Using extensive Monte Carlo simulations we study aging properties of two
disordered systems quenched below their critical point, namely the
two-dimensional random-bond Ising model and the three-dimensional
Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling
constants. We study the two-times autocorrelation and space-time correlation
functions and show that in both systems a simple aging scenario prevails in
terms of the scaling variable , where is the time-dependent
correlation length, whereas is the waiting time and is the observation
time. The investigation of the space-time correlation function for the
random-bond Ising model allows us to address some issues related to
superuniversality.Comment: 8 pages, 9 figures, to appear in European Physical Journal
Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED
Staggered fermions are constructed for the transverse lattice regularization
scheme. The weak perturbation theory of transverse lattice non-compact QED is
developed in light-cone gauge, and we argue that for fixed lattice spacing this
theory is ultraviolet finite, order by order in perturbation theory. However,
by calculating the anomalous scaling dimension of the link fields, we find that
the interaction Hamiltonian becomes non-renormalizable for ,
where is the bare (lattice) QED coupling constant. We conjecture that
this is the critical point of the chiral symmetry breaking phase transition in
QED. Non-perturbative chiral symmetry breaking is then studied in the strong
coupling limit. The discrete remnant of chiral symmetry that remains on the
lattice is spontaneously broken, and the ground state to lowest order in the
strong coupling expansion corresponds to the classical ground state of the
two-dimensional spin one-half Heisenberg antiferromagnet.Comment: 30 pages, UFIFT-HEP-92-1
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.
Parallel Excluded Volume Tempering for Polymer Melts
We have developed a technique to accelerate the acquisition of effectively
uncorrelated configurations for off-lattice models of dense polymer melts which
makes use of both parallel tempering and large scale Monte Carlo moves. The
method is based upon simulating a set of systems in parallel, each of which has
a slightly different repulsive core potential, such that a thermodynamic path
from full excluded volume to an ideal gas of random walks is generated. While
each system is run with standard stochastic dynamics, resulting in an NVT
ensemble, we implement the parallel tempering through stochastic swaps between
the configurations of adjacent potentials, and the large scale Monte Carlo
moves through attempted pivot and translation moves which reach a realistic
acceptance probability as the limit of the ideal gas of random walks is
approached. Compared to pure stochastic dynamics, this results in an increased
efficiency even for a system of chains as short as monomers, however
at this chain length the large scale Monte Carlo moves were ineffective. For
even longer chains the speedup becomes substantial, as observed from
preliminary data for
Computer Simulations of Supercooled Liquids and Glasses
After a brief introduction to the dynamics of supercooled liquids, we discuss
some of the advantages and drawbacks of computer simulations of such systems.
Subsequently we present the results of computer simulations in which the
dynamics of a fragile glass former, a binary Lennard-Jones system, is compared
to the one of a strong glass former, SiO_2. This comparison gives evidence that
the reason for the different temperature dependence of these two types of glass
formers lies in the transport mechanism for the particles in the vicinity of
T_c, the critical temperature of mode-coupling theory. Whereas the one of the
fragile glass former is described very well by the ideal version of
mode-coupling theory, the one for the strong glass former is dominated by
activated processes. In the last part of the article we review some simulations
of glass formers in which the dynamics below the glass transition temperature
was investigated. We show that such simulations might help to establish a
connection between systems with self generated disorder (e.g. structural
glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article
in J. Phys.: Condens. Matte
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