34 research outputs found
The Phase Diagrams of the Schwinger and Gross-Neveu Models with Wilson Fermions
A new method to analytically determine the partition function zeroes of
weakly coupled theories on finite-size lattices is developed. Applied to the
lattice Schwinger model, this reveals the possible absence of a phase
transition at fixed weak coupling. We show how finite-size scaling techniques
on small or moderate lattice sizes may mimic the presence of a spurious phase
transition. Application of our method to the Gross-Neveu model yields a phase
diagram consistent with that coming from a saddle point analysis.Comment: Talk at LATTICE99, 3 pages, 2 figure
On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions
There are problems in physics and particularly in field theory which are
defined by complex valued weight functions where is a polynomial
action . The conditions under which a convergent complex
Langevin calculation correctly simulates such integrals are discussed. All
conditions on the process which are used to prove proper convergence are
defined in the stationary limit.Comment: 8 pages, LaTeX file, preprint UNIGRAZ-UTP 29-09-9
Normalization of the chiral condensate in the massive Schwinger model
Within mass perturbation theory, already the first order contribution to the
chiral condensate of the massive Schwinger model is UV divergent. We discuss
the problem of choosing a proper normalization and, by making use of some
bosonization results, we are able to choose a normalization so that the
resulting chiral condensate may be compared, e.g., with lattice data.Comment: Latex file, 8 pages, 1 figure, needed macro: psbox.te
Critical Behavior of the Schwinger Model with Wilson Fermions
We present a detailed analysis, in the framework of the MFA approach, of the
critical behaviour of the lattice Schwinger model with Wilson fermions on
lattices up to , through the study of the Lee-Yang zeros and the specific
heat. We find compelling evidence for a critical line ending at
at large . Finite size scaling analysis on lattices and indicates a continuous transition. The hyperscaling relation
is verified in the explored region.Comment: 12 pages LaTeX file, 10 figures in one uuencoded compressed
postscript file. Report LNF-95/049(P
Computing Masses from Effective Transfer Matrices
We study the use of effective transfer matrices for the numerical computation
of masses (or correlation lengths) in lattice spin models. The effective
transfer matrix has a strongly reduced number of components. Its definition is
motivated by a renormalization group transformation of the full model onto a
1-dimensional spin model. The matrix elements of the effective transfer matrix
can be determined by Monte Carlo simulation. We show that the mass gap can be
recovered exactly from the spectrum of the effective transfer matrix. As a
first step towards application we performed a Monte Carlo study for the
2-dimensional Ising model. For the simulations in the broken phase we employed
a multimagnetical demon algorithm. The results for the tunnelling correlation
length are particularly encouraging.Comment: (revised version: a few references added) LaTeX file, 25 pages, 6
PostScript figures, (revised version: a few references added
Some approximate analytical methods in the study of the self-avoiding loop model with variable bending rigidity and the critical behaviour of the strong coupling lattice Schwinger model with Wilson fermions
Some time ago Salmhofer demonstrated the equivalence of the strong coupling
lattice Schwinger model with Wilson fermions to a certain 8-vertex model which
can be understood as a self-avoiding loop model on the square lattice with
bending rigidity and monomer weight . The
present paper applies two approximate analytical methods to the investigation
of critical properties of the self-avoiding loop model with variable bending
rigidity, discusses their validity and makes comparison with known MC results.
One method is based on the independent loop approximation used in the
literature for studying phase transitions in polymers, liquid helium and cosmic
strings. The second method relies on the known exact solution of the
self-avoiding loop model with bending rigidity . The present
investigation confirms recent findings that the strong coupling lattice
Schwinger model becomes critical for . The phase
transition is of second order and lies in the Ising model universality class.
Finally, the central charge of the strong coupling Schwinger model at
criticality is discussed and predicted to be .Comment: 22 pages LaTeX, 6 Postscript figure
Chiral Symmetry in Two-Color QCD at Finite Temperature
We study the chiral symmetry in two-color QCD with N massless flavors at
finite temperature, using an effective theory. For the gauge group SU(2), the
chiral symmetry is enlarged to SU(2N), which is then spontaneously broken to
Sp(2N) at zero temperature. At finite temperature, and when the axial anomaly
can be neglected, we find a first order phase transition occurring for two or
more flavors. In the presence of instantons, the symmetry restoration
unambiguously remains first order for three or more massless flavors. These
results could be relevant for lattice studies of chiral symmetry at finite
temperature and density.Comment: 10 pages, Revte
Critical Constraints on Chiral Hierarchies
We consider the constraints that critical dynamics places on models with a
top quark condensate or strong extended technicolor (ETC). These models require
that chiral-symmetry-breaking dynamics at a high energy scale plays a
significant role in electroweak symmetry breaking. In order for there to be a
large hierarchy between the scale of the high energy dynamics and the weak
scale, the high energy theory must have a second order chiral phase transition.
If the transition is second order, then close to the transition the theory may
be described in terms of a low-energy effective Lagrangian with composite
``Higgs'' scalars. However, scalar theories in which there are more than one
coupling can have a {\it first order} phase transition instead, due to
the Coleman-Weinberg instability. Therefore, top-condensate or strong ETC
theories in which the composite scalars have more than one coupling
cannot always support a large hierarchy. In particular, if the
Nambu--Jona-Lasinio model solved in the large- limit is a good
approximation to the high-energy dynamics, then these models will not produce
acceptable electroweak symmetry breaking.Comment: 10 pages, 1 postscript figure (appended), BUHEP-92-35, HUTP-92/A05
Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice
The line of phase transitions, separating the confinement and the Coulomb
phases in the four-dimensional pure compact U(1) gauge theory with extended
Wilson action, is reconsidered. We present new numerical evidence that a part
of this line, including the original Wilson action, is of second order. By
means of a high precision simulation on homogeneous lattices on a sphere we
find that along this line the scaling behavior is determined by one fixed point
with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the
existence of a nontrivial and nonasymptotically free four-dimensional pure U(1)
gauge theory in the continuum very probable. The universality and duality
arguments suggest that this conclusion holds also for the monopole loop gas,
for the noncompact abelian Higgs model at large negative squared bare mass, and
for the corresponding effective string theory.Comment: 11 pages, LaTeX, 2 figure
Universality of the Ising Model on Sphere-like Lattices
We study the 2D Ising model on three different types of lattices that are
topologically equivalent to spheres. The geometrical shapes are reminiscent of
the surface of a pillow, a 3D cube and a sphere, respectively. Systems of
volumes ranging up to O() sites are simulated and finite size scaling is
analyzed. The partition function zeros and the values of various cumulants at
their respective peak positions are determined and they agree with the scaling
behavior expected from universality with the Onsager solution on the torus
(). For the pseudocritical values of the coupling we find significant
anomalies indicating a shift exponent for sphere-like lattice
topology.Comment: 24 pages, LaTeX, 8 figure