1,476 research outputs found
Four-loop contributions to long-distance quantities in the two-dimensional nonlinear sigma-model on a square lattice: revised numerical estimates
We give the correct analytic expression of a finite integral appearing in the
four-loop computation of the renormalization-group functions for the
two-dimensional nonlinear sigma-model on the square lattice with standard
action, explaining the origin of a numerical discrepancy. We revise the
numerical expressions of Caracciolo and Pelissetto for the perturbative
corrections of the susceptibility and of the correlation length. For the values
used in Monte Carlo simulations, N=3, 4, 8, the second perturbative correction
coefficient of the correlation length varies by 3%, 4%, 3% respectively. Other
quantities vary similarly.Comment: 2 pages, Revtex, no figure
Lattice energy-momentum tensor with Symanzik improved actions
We define the energy-momentum tensor on lattice for the and
for the nonlinear -model Symanzik tree-improved actions, using Ward
identities or an explicit matching procedure. The resulting operators give the
correct one loop scale anomaly, and in the case of the sigma model they can
have applications in Monte Carlo simulations.Comment: Self extracting archive fil
The critical region of strong-coupling lattice QCD in different large-N limits
We study the critical behavior at nonzero temperature phase transitions of an
effective Hamiltonian derived from lattice QCD in the strong-coupling
expansion. Following studies of related quantum spin systems that have a
similar Hamiltonian, we show that for large and fixed , mean
field scaling is not expected, and that the critical region has a finite width
at . A different behavior rises for and fixed
and , which we study in two spatial dimensions and for . We
find that the width of the critical region is suppressed by with
, and argue that a generalization to and to three dimensions
will change this only in detail (e.g. the value of ), but not in
principle. We conclude by stating under what conditions this suppression is
expected, and remark on possible realizations of this phenomenon in lattice
gauge theories in the continuum.Comment: 24 pages, 6 figures. New version includes: a more extensive
discussion of strong-coupling expansions and their region of validity.
Accordingly I have reworded the descriptions of the investigated limits.
Removed typos and misprint
de Sitter gravity from lattice gauge theory
We investigate a lattice model for Euclidean quantum gravity based on
discretization of the Palatini formulation of General Relativity. Using Monte
Carlo simulation we show that while a naive approach fails to lead to a vacuum
state consistent with the emergence of classical spacetime, this problem may be
evaded if the lattice action is supplemented by an appropriate counter term. In
this new model we find regions of the parameter space which admit a ground
state which can be interpreted as (Euclidean) de Sitter space.Comment: 16 pages, 11 figures. email address update
Critical Behavior of the Two-Dimensional Randomly Driven Lattice Gas
We investigate the critical behavior of the two-dimensional randomly driven
lattice gas, in which particles are driven along one of the lattice axes by an
infinite external field with randomly changing sign. A finite-size scaling
(FSS) analysis provides novel evidences that this model is not in the same
universality class as the driven lattice gas with a constant drive (DLG),
contrarily to what has been recently reported in the literature. Indeed, the
FSS functions of transverse observables (i.e., related to order-parameter
fluctuations with wave vector perpendicular to the direction of the field)
differ from the mean-field behavior predicted and observed within the DLG
universality class. At variance with the DLG case, FSS is attained on lattices
with fixed aspect ratio and anisotropy exponent equal to 1 and the transverse
Binder cumulant does not vanish at the critical point.Comment: 4 pages, 4 figure
Gauged O(n) spin models in one dimension
We consider a gauged O(n) spin model, n >= 2, in one dimension which contains
both the pure O(n) and RP(n-1) models and which interpolates between them. We
show that this model is equivalent to the non-interacting sum of the O(n) and
Ising models. We derive the mass spectrum that scales in the continuum limit,
and demonstrate that there are two universality classes, one of which contains
the O(n) and RP(n-1) models and the other which has a tuneable parameter but
which is degenerate in the sense that it arises from the direct sum of the O(n)
and Ising models.Comment: 9 pages, no figures, LaTeX sourc
Universality Class of Models
We point out that existing numerical data on the correlation length and
magnetic susceptibility suggest that the two dimensional model with
standard action has critical exponent , which is inconsistent with
asymptotic freedom. This value of is also different from the one of the
Wess-Zumino-Novikov-Witten model that is supposed to correspond to the
model at .Comment: 8 pages, with 3 figures included, postscript. An error concerning the
errors has been correcte
On the question of universality in \RPn and \On Lattice Sigma Models
We argue that there is no essential violation of universality in the
continuum limit of mixed \RPn and \On lattice sigma models in 2 dimensions,
contrary to opposite claims in the literature.Comment: 16 pages (latex) + 3 figures (Postscript), uuencode
General duality for abelian-group-valued statistical-mechanics models
We introduce a general class of statistical-mechanics models, taking values
in an abelian group, which includes examples of both spin and gauge models,
both ordered and disordered. The model is described by a set of ``variables''
and a set of ``interactions''. A Gibbs factor is associated to each variable
and to each interaction. We introduce a duality transformation for systems in
this class. The duality exchanges the abelian group with its dual, the Gibbs
factors with their Fourier transforms, and the interactions with the variables.
High (low) couplings in the interaction terms are mapped into low (high)
couplings in the one-body terms. The idea is that our class of systems extends
the one for which the classical procedure 'a la Kramers and Wannier holds, up
to include randomness into the pattern of interaction. We introduce and study
some physical examples: a random Gaussian Model, a random Potts-like model, and
a random variant of discrete scalar QED. We shortly describe the consequence of
duality for each example.Comment: 26 pages, 2 Postscript figure
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