7,787 research outputs found
A cluster algorithm for Lattice Gauge Theories
A new algorithm for simulating compact U(1) lattice gauge theory in three
dimensions is presented which is based on global changes in the configuration
space. We show that this algorithm provides an effective way to extract
partition functions at given external flux. As an application, we study
numerically the finite temperature deconfinement phase transition.Comment: 4 pages, 2 figures. Talk given at the Conference on Computational
Physics, Genova, Italy, Sept. 200
Chiral Limit of Strongly Coupled Lattice Gauge Theories
We construct a new and efficient cluster algorithm for updating strongly
coupled U(N) lattice gauge theories with staggered fermions in the chiral
limit. The algorithm uses the constrained monomer-dimer representation of the
theory and should also be of interest to researchers working on other models
with similar constraints. Using the new algorithm we address questions related
to the chiral limit of strongly coupled U(N) gauge theories beyond the mean
field approximation. We show that the infinite volume chiral condensate is
non-zero in three and four dimensions. However, on a square lattice of size
we find for large
where . These results differ from an
earlier conclusion obtained using a different algorithm. Here we argue that the
earlier calculations were misleading due to uncontrolled autocorrelation times
encountered by the previous algorithm.Comment: 36 Pages, 9 figures, aps revtex forma
D-Theory: Field Theory via Dimensional Reduction of Discrete Variables
A new non-perturbative approach to quantum field theory --- D-theory --- is
proposed, in which continuous classical fields are replaced by discrete
quantized variables which undergo dimensional reduction. The 2-d classical O(3)
model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of
quantum spins. Dimensional reduction is demonstrated explicitly by simulating
correlation lengths up to 350,000 lattice spacings using a loop cluster
algorithm. In the framework of D-theory, gauge theories are formulated in terms
of quantum links --- the gauge analogs of quantum spins. Quantum links are
parallel transporter matrices whose elements are non-commuting operators. They
can be expressed as bilinears of anticommuting fermion constituents. In quantum
link models dimensional reduction to four dimensions occurs, due to the
presence of a 5-d Coulomb phase, whose existence is confirmed by detailed
simulations using standard lattice gauge theory. Using Shamir's variant of
Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of
a 5-d slab. This naturally protects their chiral symmetries without
fine-tuning. The first efficient cluster algorithm for a gauge theory with a
continuous gauge group is formulated for the U(1) quantum link model. Improved
estimators for Wilson loops are constructed, and dimensional reduction to
ordinary lattice QED is verified numerically.Comment: 15 pages, LaTeX, including 9 encapsulated postscript figures.
Contribution to Lattice 97 by 5 authors, to appear in Nuclear Physics B
(Proceeding Supplements). Requires psfig.tex and espcrc2.st
Kosterlitz Thouless Universality in Dimer Models
Using the monomer-dimer representation of strongly coupled U(N) lattice gauge
theories with staggered fermions, we study finite temperature chiral phase
transitions in (2+1) dimensions. A new cluster algorithm allows us to compute
monomer-monomer and dimer-dimer correlations at zero monomer density (chiral
limit) accurately on large lattices. This makes it possible to show
convincingly, for the first time, that these models undergo a finite
temperature phase transition which belongs to the Kosterlitz-Thouless
universality class. We find that this universality class is unaffected even in
the large N limit. This shows that the mean field analysis often used in this
limit breaks down in the critical region.Comment: 4 pages, 4 figure
Progress in Lattice Field Theory Algorithms
I present a summary of recent algorithmic developments for lattice field
theories. In particular I give a pedagogical introduction to the new
Multicanonical algorithm, and discuss the relation between the Hybrid
Overrelaxation and Hybrid Monte Carlo algorithms. I also attempt to clarify the
role of the dynamical critical exponent z and its connection with
`computational cost.' [Includes four PostScript figures]Comment: 27 page
Quantum Link Models: A Discrete Approach to Gauge Theories
We construct lattice gauge theories in which the elements of the link
matrices are represented by non-commuting operators acting in a Hilbert space.
These quantum link models are related to ordinary lattice gauge theories in the
same way as quantum spin models are related to ordinary classical spin systems.
Here U(1) and SU(2) quantum link models are constructed explicitly. As
Hamiltonian theories quantum link models are nonrelativistic gauge theories
with potential applications in condensed matter physics. When formulated with a
fifth Euclidean dimension, universality arguments suggest that dimensional
reduction to four dimensions occurs. Hence, quantum link models are also
reformulations of ordinary quantum field theories and are applicable to
particle physics, for example to QCD. The configuration space of quantum link
models is discrete and hence their numerical treatment should be simpler than
that of ordinary lattice gauge theories with a continuous configuration space.Comment: 18 pages, Latex, no figures, final version to appear in Nuclear
Physics B, references to earlier work by Horn, Orland and Rohrlich include
- …