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Sergio Caracciolo

Publications and source records attributed to Sergio Caracciolo.

At least 109 records · Page 6Linked to original sources
arXiv1998

Crossover scaling from classical to non-classical critical behaviour

Interacting physical systems in the neighborhood of criticality (and massive continuum field theories) can often be characterized by just two physical scales: a (macroscopic) correlation length and a (microscopic) interaction range, related to the coupling and measured by the Ginzburg number $G$. A critical crossover limit can be defined when both scales become large while their ratio stays finite. The corresponding scaling functions are universal, and they are related to the standard field-theory renormalization-group functions. The critical crossover describes the unique flow from the Gaussian to the nonclassical fixed point.

hep-lat↗
arXiv1998

Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N

We compute the corrections to finite-size scaling for the N-vector model on the square lattice in the large-N limit. We find that corrections behave as log L/L^2. For tree-level improved hamiltonians corrections behave as 1/L^2. In general l-loop improvement is expected to reduce this behaviour to 1/(L^2 \log^l L). We show that the finite-size-scaling and the perturbative limit do not commute in the calculation of the corrections to finite-size scaling. We present also a detailed study of the corrections for the RP^N-model.

hep-lat↗
arXiv1998

Use of even Grassmann variables to construct effective actions for mesons

A quadratic action in even Grassmann variables with the quantum numbers of the pions has been studied. It includes the $σ$-field in order to be invariant under SU(2)_L times SU(2)_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.

hep-lat↗
arXiv1998

A free action for pions as quark composites

In the framework of an approach to bosonization based on the use of fermionic composites as fundamental variables, a quadratic action in even Grassmann variables with the quantum numbers of the pions has been constructed. It includes the sigma-field in order to be invariant under SU(2)_L times SU(2)]_R transformations over the quarks. This action exhibits the Goldstone phenomenon reducing its symmetry to the O(3) isospin invariance. A squared mass for the pions is generated according to PCAC. The model has been investigated in the Stratonovitch-Hubbard representation, in which form it is reminiscent of the Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in inverse powers of the index of nilpotency of the mesonic fields (which is 24), is generated. The way it might be used in a new perturbative approach to QCD is outlined.

hep-ph↗
arXiv1997

Monte Carlo results for three-dimensional self-avoiding walks

We discuss possible sources of systematic errors in the computation of critical exponents by renormalization-group methods, extrapolations from exact enumerations and Monte Carlo simulations. A careful Monte Carlo determination of the susceptibility exponent gamma for three-dimensional self-avoiding walks has been used to test the claimed accuracy of the various methods.

hep-lat↗
arXiv1997

Improved actions for the two-dimensional sigma-model

For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an elementary plaquette. We show the large N solution and preliminary Monte Carlo results for N=3.

hep-lat↗
arXiv1996

Comparing Different Improvement Programs for the N-Vector Model

We discuss the connection between various types of improved actions in the context of the two-dimensional sigma-model. We also discuss spectrum-improved actions showing that these actions do not have any improved behaviour. An O(a^2) on-shell improved action with all couplings defined on a plaquette and satisfying reflection positivity is also explicitly constructed.

hep-lat↗
arXiv1996

Corrections to finite-size scaling in two-dimensional O(N) sigma-models

We have considered the corrections to the finite-size-scaling functions for a general class of $O(N)$ $σ$-models with two-spin interactions in two dimensions for $N=\infty$. We have computed the leading corrections finding that they generically behave as $(f(z) \log L + g(z))/L^2$ where $z = m(L) L$ and $m(L)$ is a mass scale; $f(z)$ vanishes for Symanzik improved actions for which the inverse propagator behaves as $q^2 + O(q^6)$ for small $q$, but not for on-shell improved ones. We also discuss a model with four-spin interactions which shows a much more complicated behaviour.

hep-lat↗
arXiv1996

How to compute one-loop Feynman diagrams in lattice QCD with Wilson fermions

We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of L\" uscher and Weisz to higher-loop integrals with fermions.

hep-lat↗
arXiv1996

Algebraic algorithm for the computation of one-loop Feynman diagrams in lattice QCD with Wilson fermions

We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions.

hep-lat↗
arXiv1995

Four-Loop Perturbative Expansion for the Lattice $N$-Vector Model

We compute the four-loop contributions to the $β$-function and the anomalous dimension of the field for the $O(N)$-invariant $N$-vector model. These results are used to compute the second analytic corrections to the correlation length and the general spin-$n$ susceptibility.

hep-lat↗
arXiv1995

Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional $N$-Vector Model for $N=3,4,8$

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N = 3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.

hep-lat↗
arXiv1994

New Method for the Extrapolation of Finite-Size Data to Infinite Volume

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $σ$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

hep-lat↗