Critical exponents of a three dimensional O(4) spin model

By Monte Carlo simulation we study the critical exponents governing the transition of the three-dimensional classical O(4) Heisenberg model, which is considered to be in the same universality class as the finite-temperature QCD with massless two flavors. We use the single cluster algorithm and the histogram reweighting technique to obtain observables at the critical temperature. After estimating an accurate value of the inverse critical temperature \Kc=0.9360(1), we make non-perturbative estimates for various critical exponents by finite-size scaling analysis. They are in excellent agreement with those obtained with the $4-\epsilon$ expansion method with errors reduced to about halves of them.Comment: 25 pages with 8 PS figures, LaTeX, UTHEP-28

Radio-quiet and radio-loud pulsars: similar in Gamma-rays but different in X-rays

We present new Chandra and XMM-Newton observations of a sample of eight radio-quiet Gamma-ray pulsars detected by the Fermi Large Area Telescope. For all eight pulsars we identify the X-ray counterpart, based on the X-ray source localization and the best position obtained from Gamma-ray pulsar timing. For PSR J2030+4415 we found evidence for an about 10 arcsec-long pulsar wind nebula. Our new results consolidate the work from Marelli et al. 2011 and confirm that, on average, the Gamma-ray--to--X-ray flux ratios (Fgamma/Fx) of radio-quiet pulsars are higher than for the radio-loud ones. Furthermore, while the Fgamma/Fx distribution features a single peak for the radio-quiet pulsars, the distribution is more dispersed for the radio-loud ones, possibly showing two peaks. We discuss possible implications of these different distributions based on current models for pulsar X-ray emission.Comment: Accepted for publication in The Astrophysical Journal; 12 pages, 3 figures, 2 table

A Swendsen-Wang update algorithm for the Symanzik improved sigma model

We study a generalization of Swendsen-Wang algorithm suited for Potts models with next-next-neighborhood interactions. Using the embedding technique proposed by Wolff we test it on the Symanzik improved bidimensional non-linear $\sigma$ model. For some long range observables we find a little slowing down exponent ($z \simeq 0.3$) that we interpret as an effect of the partial frustration of the induced spin model.Comment: Self extracting archive fil

Energy Distribution in disordered elastic Networks

Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed

Gradual Certified Programming in Coq

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion a la gradual typing. Additionally, when extracting Coq functions to mainstream languages, our encoding of casts supports lifting assumed properties into runtime checks. Much to our surprise, it is not necessary to extend Coq in any way to support gradual certified programming. A simple mix of type classes and axioms makes it possible to bring gradual certified programming to Coq in a straightforward manner.Comment: DLS'15 final version, Proceedings of the ACM Dynamic Languages Symposium (DLS 2015

The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change

Tests of the continuum limit for the SO(4)SO(4) Principal Chiral Model and the prediction for \L_\MS

We investigate the continuum limit in $SO(N)$ Principal Chiral Models concentrating in detail on the $SO(4)$ model and its covering group SU(2)xSU(2). We compute the mass gap in terms of Lambda_MS and compare with the prediction of Hollowood of m/\L_\MS = 3.8716. We use the finite-size scaling method of L\"uscher et al. to deduce m/\L_\MS and find that for the $SO(4)$ model the computed result of m/\L_\MS \sim 14 is in strong disagreement with theory but that a similar analysis of the SU(2)xSU(2) yields excellent agreement with theory. We conjecture that for $SO(4)$ violations of the finite-size scaling assumption are severe forthe values of the correlation length, $\xi$, investigated and that our attempts to extrapolate the results to zero lattice spacing, although plausible, are erroneous. Conversely, the finite-size scaling violations in the SU(2)xSU(2) simulation are consistent with perturbation theory and the computed $beta-$function agrees well with the 3-loop approximation for couplings evaluated at scales $L/a \le \xi$, where $\xi$ is measured in units of the lattice spacing, $a$. We conjecture that lattice vortex artifacts in the $SO(4)$ model are responsible for delaying the onset of the continuum limit until much larger correlation lengths are achieved notwithstanding the apparent onset of scaling. Results for the mass spectrum for SO(N) m, N=8,10 are given whose comparison with theory gives plausible support to our ideas.Comment: 27 pages , 1 Postscript-file, uuencode

Cluster algorithms

Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster and single--cluster methods, and of the standard and improved estimators are compared. (Lecture given at the summer school on `Advances in Computer Simulations', Budapest, July 1996.)Comment: 17 pages, Late

Testing fixed points in the 2D O(3) non-linear sigma model

Using high statistic numerical results we investigate the properties of the O(3) non-linear 2D sigma-model. Our main concern is the detection of an hypothetical Kosterlitz-Thouless-like (KT) phase transition which would contradict the asymptotic freedom scenario. Our results do not support such a KT-like phase transition.Comment: Latex, 7 pgs, 4 eps-figures. Added more analysis on the KT-transition. 4-loop beta function contains corrections from D.-S.Shin (hep-lat/9810025). In a note-added we comment on the consequences of these corrections on our previous reference [16