arXiv subjects
Publications and source records attributed to Sergio Caracciolo.
We test an algebraic algorithm based on the coordinate-space method, evaluating with high accuracy the critical mass for Wilson fermions in lattice QCD at two loops. We test the results by using different types of infrared regularization.
We consider a two-dimensional sigma-model with discrete icosahedral/dodecahedral symmetry. We present high-precision finite-size numerical results that show that the continuum limit of this model is different from the continuum limit of the rotationally invariant O(3) sigma-model.
We have redone a recent two-loop computation of the critical mass for Wilson fermions in lattice QCD by evaluating Feynman integrals with the coordinate-space method. We present the results for different types of infrared regularization. We confirm both the previous numerical estimates and the power of the coordinate-space method whenever high accuracy is needed.
We present a detailed Monte Carlo study of the high-temperature phase of the two-dimensional driven lattice gas at infinite driving field. We define a finite-volume correlation length, study its finite-size-scaling behavior and extrapolate it to the infinite-volume limit by using an iterative extrapolation method. The same method is applied to the susceptibility. We determine the transverse exponents $γ$ and $ν$. They turn out to be in perfect agreement with the theoretical predictions. We also compute the transverse Binder parameter, which apparently vanishes at the critical point, and the distribution of the magnetization. These results confirm the Gaussian nature of the transverse excitations.
We study the two-dimensional renormalization-group flow induced by perturbations that reduce the global symmetry of the O(3) sigma-model to the discrete symmetries of Platonic solids. We estimate the value of the correlation length at which differences in the behaviour of the various models should be expected. For the icosahedron model, we find xi > 200. We provide an explanation for the recent numerical results of Patrascioiu and Seiler and of Hasenfratz and Niedermayer.
We address the problem of the definition of the finite-volume correlation length. First, we study the large-N limit of the N-vector model, and we show the existence of several constraints on the definition if regularity of the finite-size scaling functions and correct anomalous behaviour above the upper critical dimension are required. Then, we study in detail a model in which the zero mode in prohibited. Such a model is a generalization of the fixed-magnetization Ising model which is equivalent to the lattice gas. Also in this case, we find that the finite-volume correlation length must satisfy appropriate constraints in order to obtain regular finite-size scaling functions, and, above the upper critical dimension, an anomalous scaling behaviour. The large-N results are confirmed by a one-loop calculation in the lattice $ϕ^4$ theory.
The standard QCD action is improved by the addition of irrelevant operators built with chiral composites. An effective Lagrangian is derived in terms of auxiliary fields, which has the form of the phenomenological chiral Lagrangians. Our improved QCD action appears promising for numerical simulations as the pion physics is explicitely accounted for by the auxiliary fields.
We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m a \approx 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the possible systematic errors.
We evaluate the pion_0 into two gammas decay amplitude by an effective action derived from QCD in the quark composites approach, getting the standard value. We also verify that our effective action correctly reproduces the chiral anomaly.
We study the end-to-end distribution function for dilute polymers. We present a computation to order $O(ε^2)$, $ε= 4 - d$, and discuss in detail its asymptotic behaviour for small and large distances. The theoretical predictions are compared with Monte Carlo results, finding good agreement.
We study the 3D Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Using an iterative extrapolation procedure, Monte Carlo data are extrapolated to infinite volume up to correlation length ξ= 140. The infinite volume data are consistent with both a continuous phase transition at finite temperature and an essential singularity at finite temperature. An essential singularity at zero temperature is excluded.
We introduce several bilocal algorithms for lattice self-avoiding walks that provide reasonable models for the physical kinetics of polymers in the absence of hydrodynamic effects. We discuss their ergodicity in different confined geometries, for instance in strips and in slabs. A short discussion of the dynamical properties in the absence of interactions is given.
The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of systematic errors. The key problem turns out to be the violation of asymptotic scaling.
We study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Monte Carlo data are extrapolated to infinite volume with an iterative procedure up to correlation lengths xi \approx 140. The infinite volume data are consistent with a conventional power law singularity at finite temperature Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015, nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an exponential singularity at finite Tc, but not with an exponential singularity at zero temperature.
We present a high-statistics Monte Carlo determination of the exponent gamma for self-avoiding walks on a Manhattan lattice in two dimensions. A conservative estimate is $γ\gtapprox 1.3425(3)$, in agreement with the universal value 43/32 on regular lattices, but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations. We find strong corrections to scaling that seem to indicate the presence of a non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma = 1.3436(3), where the error is purely statistical.
We study the finite-size behaviour of a tree-level on-shell improved action for the N-vector model. We present numerical results for N=3 and analytic results in the large-N limit for the mass gap. We also report a perturbative computation at one loop of the mass gap for states of spatial momentum p. We present a detailed comparison of the behaviour of this action with that of other formulations, including the perfect action, and a critical discussion of the different approaches to the problem of action improvement.
We present a perturbative approach to QCD based on quark composites, that is barions and mesons, as fundamental variables.
It has been recently proposed to use the operator product expansion to evaluate the expectation values of renormalized operators without the need of a direct computation of the relevant renormalization constants. We test the viability of this idea in the two-dimensional non-linear sigma-model discussing the non-perturbative renormalization of the energy-momentum tensor.