185 research outputs found
Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
We report on an ongoing project to parametrize the Fixed-Point Dirac operator
for massless quarks, using a very general construction which has arbitrarily
many fermion offsets and gauge paths, the complete Clifford algebra and
satisfies all required symmetries. Optimizing a specific construction with
hypercubic fermion offsets, we present some preliminary results.Comment: Lattice 2000 (Improvement), 9 pages, based on a talk by K.H. and a
poster by T.J. References adde
Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
We investigate the cutoff effects in 2-d lattice O(N) models for a variety of
lattice actions, and we identify a class of very simple actions for which the
lattice artifacts are extremely small. One action agrees with the standard
action, except that it constrains neighboring spins to a maximal relative angle
delta. We fix delta by demanding that a particular value of the step scaling
function agrees with its continuum result already on a rather coarse lattice.
Remarkably, the cutoff effects of the entire step scaling function are then
reduced to the per mille level. This also applies to the theta-vacuum effects
of the step scaling function in the 2-d O(3) model. The cutoff effects of other
physical observables including the renormalized coupling and the mass in the
isotensor channel are also reduced drastically. Another choice, the mixed
action, which combines the standard quadratic with an appropriately tuned large
quartic term, also has extremely small cutoff effects. The size of cutoff
effects is also investigated analytically in 1-d and at N = infinity in 2-d.Comment: 39 pages, 18 figure
The construction of generalized Dirac operators on the lattice
We discuss the steps to construct Dirac operators which have arbitrary
fermion offsets, gauge paths, a general structure in Dirac space and satisfy
the basic symmetries (gauge symmetry, hermiticity condition, charge
conjugation, hypercubic rotations and reflections) on the lattice. We give an
extensive set of examples and offer help to add further structures.Comment: 19 pages, latex, maple code attache
Lattice Theories with Nonlinearly Realized Chiral Symmetry
We present the lattice formulation of effective Lagrangians in which chiral
symmetry is realized nonlinearly on the fermion fields. In this framework both
the Wilson term removing unphysical doubler fermions and the fermion mass term
do not break chiral symmetry. Our lattice formulation allows us to address
non-perturbative questions in effective theories of baryons interacting with
pions and in models involving constitutent quarks interacting with pions and
gluons. With the presented methods, a system containing a non-zero density of
static baryons interacting with pions can be studied on the lattice without
encountering a complex action problem. This might lead to new insights into the
phase diagram of strongly interacting matter at non-zero chemical potential.Comment: 3 pages, Lattice2003(chiral
Cluster algorithms
Cluster algorithms for classical and quantum spin systems are discussed. In
particular, the cluster algorithm is applied to classical O(N) lattice actions
containing interactions of more than two spins. The performance of the
multi-cluster and single--cluster methods, and of the standard and improved
estimators are compared. (Lecture given at the summer school on `Advances in
Computer Simulations', Budapest, July 1996.)Comment: 17 pages, Late
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