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Search Results: 1 - 10 of 10121 matches for " Sergio Caracciolo "
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Comparing Different Improvement Programs for the N-Vector Model
Sergio Caracciolo,Andrea Pelissetto
Physics , 1996, DOI: 10.1016/S0370-2693(97)00495-4
Abstract: 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.
Corrections to Finite-Size Scaling in the Lattice N-Vector Model for Infinite N
Sergio Caracciolo,Andrea Pelissetto
Physics , 1998, DOI: 10.1103/PhysRevD.58.105007
Abstract: 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.
Universal Finite Size Scaling Functions in the 3D Ising Spin Glass
Matteo Palassini,Sergio Caracciolo
Physics , 1999, DOI: 10.1103/PhysRevLett.82.5128
Abstract: 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.
Lattice Perturbation Theory for $O(N)$-Symmetric $σ$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory
Sergio Caracciolo,Andrea Pelissetto
Physics , 1994, DOI: 10.1016/0550-3213(94)90378-6
Abstract: We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop beta-function. These results are used to compute the first analytic corrections to various long-distance quantities as the correlation length and the general spin-$n$ susceptibility. It is found that these corrections are extremely large for $RP^{N-1}$ models (especially for small values of N), so that asymptotic scaling can be observed in these models only at very large values of beta. We also give the first three terms in the asymptotic expansion of the vector and tensor energies.
Corrections to finite-size scaling in two-dimensional O(N) sigma-models
Sergio Caracciolo,Andrea Pelissetto
Physics , 1996, DOI: 10.1016/S0920-5632(96)00756-6
Abstract: We have considered the corrections to the finite-size-scaling functions for a general class of $O(N)$ $\sigma$-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.
Four-Loop Perturbative Expansion for the Lattice $N$-Vector Model
Sergio Caracciolo,Andrea Pelissetto
Physics , 1995, DOI: 10.1016/0550-3213(95)00438-X
Abstract: We compute the four-loop contributions to the $\beta$-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.
An exactly solvable random satisfiability problem
Sergio Caracciolo,Andrea Sportiello
Physics , 2002, DOI: 10.1088/0305-4470/35/36/301
Abstract: We introduce a new model for the generation of random satisfiability problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt and Zecchina, which is a variant of the famous K-SAT model: it is extended to q-state variables and relates to a different choice of the statistical ensemble. The model has an exactly solvable statistic: the critical exponents and scaling functions of the SAT/UNSAT transition are calculable at zero temperature, with no need of replicas, also with exact finite-size corrections. We also introduce an exact duality of the model, and show an analogy of thermodynamic properties with the Random Energy Model of disordered spin systems theory. Relations with Error-Correcting Codes are also discussed.
The pion_0 to gamma gamma decay and the chiral anomaly in the quark-composites approach to QCD
Sergio Caracciolo,Fabrizio Palumbo
Physics , 2000,
Abstract: 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.
Spanning Forests on Random Planar Lattices
Sergio Caracciolo,Andrea Sportiello
Physics , 2009, DOI: 10.1007/s10955-009-9733-1
Abstract: The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q -> 0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model in the limit n -> -1, the expansion parameter t counting the number of components in the forest. We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k = 3, a correspondence is found with the Kostov solution of the loop-gas problem, which arise as a reformulation of the (logarithmic action) O(n) model, at n = -2. Then, we show how to perform an expansion around the t = 0 theory. In the thermodynamic limit, at any order in t we have a finite sum of finite-dimensional Cauchy integrals. The leading contribution comes from a peculiar class of terms, for which a resummation can be performed exactly.
Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions
Sergio Caracciolo,Gabriele Sicuro
Physics , 2015, DOI: 10.1103/PhysRevE.91.062125
Abstract: We analyze the random Euclidean bipartite matching problem on the hypertorus in $d$ dimensions with quadratic cost and we derive the two--point correlation function for the optimal matching, using a proper ansatz introduced by Caracciolo et al. to evaluate the average optimal matching cost. We consider both the grid--Poisson matching problem and the Poisson--Poisson matching problem. We also show that the correlation function is strictly related to the Green's function of the Laplace operator on the hypertorus.
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