2,989 research outputs found
Frustrating and Diluting Dynamical Lattice Ising Spins
We investigate what happens to the third order ferromagnetic phase transition
displayed by the Ising model on various dynamical planar lattices (ie coupled
to 2D quantum gravity) when we introduce annealed bond disorder in the form of
either antiferromagnetic couplings or null couplings. We also look at the
effect of such disordering for the Ising model on general and
Feynman diagrams.Comment: 7pages, LaTex , LPTHE-ORSAY-94-5
The Spectrum of the 2+1 Dimensional Gauge Ising Model
We present a high precision Monte Carlo study of the spectrum of the
gauge theory in dimensions in the strong coupling phase. Using state of
the art Monte Carlo techniques we are able to accurately determine up to three
masses in a single channel. We compare our results with the strong coupling
expansion for the lightest mass and with results for the universal ratio
determined for the -theory. Finally the whole spectrum is
compared with that obtained from the Isgur-Paton flux tube model and the
spectrum of the dimensional gauge theory. A remarkable agreement
between the Ising and SU(2) spectra (except for the lowest mass state) is
found.Comment: uuencoded latex file of 22 pages plus 4 ps figure
Criticality in correlated quantum matter
At quantum critical points (QCP)
\cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1
994,Coleman:2005} there are quantum fluctuations on all length scales, from
microscopic to macroscopic lengths, which, remarkably, can be observed at
finite temperatures, the regime to which all experiments are necessarily
confined. A fundamental question is how high in temperature can the effects of
quantum criticality persist? That is, can physical observables be described in
terms of universal scaling functions originating from the QCPs? Here we answer
these questions by examining exact solutions of models of correlated systems
and find that the temperature can be surprisingly high. As a powerful
illustration of quantum criticality, we predict that the zero temperature
superfluid density, , and the transition temperature, , of
the cuprates are related by , where the exponent
is different at the two edges of the superconducting dome, signifying the
respective QCPs. This relationship can be tested in high quality crystals.Comment: Final accepted version not including minor stylistic correction
Ising Spins on Thin Graphs
The Ising model on ``thin'' graphs (standard Feynman diagrams) displays
several interesting properties. For ferromagnetic couplings there is a mean
field phase transition at the corresponding Bethe lattice transition point. For
antiferromagnetic couplings the replica trick gives some evidence for a spin
glass phase. In this paper we investigate both the ferromagnetic and
antiferromagnetic models with the aid of simulations. We confirm the Bethe
lattice values of the critical points for the ferromagnetic model on
and graphs and examine the putative spin glass phase in the
antiferromagnetic model by looking at the overlap between replicas in a
quenched ensemble of graphs. We also compare the Ising results with those for
higher state Potts models and Ising models on ``fat'' graphs, such as those
used in 2D gravity simulations.Comment: LaTeX 13 pages + 9 postscript figures, COLO-HEP-340,
LPTHE-Orsay-94-6
Thermally fluctuating superconductors in two dimensions
We describe the different regimes of finite temperature dynamics in the
vicinity of a zero temperature superconductor to insulator quantum phase
transition in two dimensions. New results are obtained for a low temperature
phase-only hydrodynamics, and for the intermediate temperature quantum-critical
region. In the latter case, we obtain a universal relationship between the
frequency-dependence of the conductivity and the value of the d.c. resistance.Comment: Presentation completely revised; 4 pages, 2 figure
Mean Field Behavior of Cluster Dynamics
The dynamic behavior of cluster algorithms is analyzed in the classical mean
field limit. Rigorous analytical results below establish that the dynamic
exponent has the value for the Swendsen-Wang algorithm and
for the Wolff algorithm.
An efficient Monte Carlo implementation is introduced, adapted for using
these algorithms for fully connected graphs. Extensive simulations both above
and below demonstrate scaling and evaluate the finite-size scaling
function by means of a rather impressive collapse of the data.Comment: Revtex, 9 pages with 7 figure
Dynamics and transport near quantum-critical points
The physics of non-zero temperature dynamics and transport near
quantum-critical points is discussed by a detailed study of the O(N)-symmetric,
relativistic, quantum field theory of a N-component scalar field in spatial
dimensions. A great deal of insight is gained from a simple, exact solution of
the long-time dynamics for the N=1 d=1 case: this model describes the critical
point of the Ising chain in a transverse field, and the dynamics in all the
distinct, limiting, physical regions of its finite temperature phase diagram is
obtained. The N=3, d=1 model describes insulating, gapped, spin chain
compounds: the exact, low temperature value of the spin diffusivity is
computed, and compared with NMR experiments. The N=3, d=2,3 models describe
Heisenberg antiferromagnets with collinear N\'{e}el correlations, and
experimental realizations of quantum-critical behavior in these systems are
discussed. Finally, the N=2, d=2 model describes the superfluid-insulator
transition in lattice boson systems: the frequency and temperature dependence
of the the conductivity at the quantum-critical coupling is described and
implications for experiments in two-dimensional thin films and inversion layers
are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical
properties of unconventional magnetic systems", Geilo, Norway, April 2-12,
1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be
published. 46 page
Adjoint Wilson Line in SU(2) Lattice Gauge Theory
The behavior of the adjoint Wilson line in finite-temperature, ,
lattice gauge theory is discussed. The expectation value of the line and the
associated excess free energy reveal the response of the finite-temperature
gauge field to the presence of an adjoint source. The value of the adjoint line
at the critical point of the deconfining phase transition is highlighted. This
is not calculable in weak or strong coupling. It receives contributions from
all scales and is nonanalytic at the critical point. We determine the general
form of the free energy. It includes a linearly divergent term that is
perturbative in the bare coupling and a finite, nonperturbative piece. We use a
simple flux tube model to estimate the value of the nonperturbative piece. This
provides the normalization needed to estimate the behavior of the line as one
moves along the critical curve into the weak coupling region.Comment: 21 pages, no figures, Latex/Revtex 3, UCD-93-1
Three "universal" mesoscopic Josephson effects
1. Introduction
2. Supercurrent from Excitation Spectrum
3. Excitation Spectrum from Scattering Matrix
4. Short-Junction Limit
5. Universal Josephson Effects
5.1 Quantum Point Contact
5.2 Quantum Dot
5.3 Disordered Point Contact (Average supercurrent, Supercurrent
fluctuations)Comment: 21 pages, 2 figures; legacy revie
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