HEP Lattice·hep-lat
7 papers—4 primary·3 cross-listed·reconstructed*
qq+q Collaboration · F. Farchioni · C. Gebert · I. Montvay · L. Scorzato
The computational cost of numerical simulations of QCD with light dynamical Wilson-quarks is estimated. The qualitative behaviour of the pion mass and coupling at small quark masses is discussed.
With the exception of confinement the three-dimensional Nambu-Jona-Lasinio (NJL_3) model incorporates many of the essential properties of QCD. We discuss the critical properties of the model at nonzero temperature T and/or nonzero chemical potential . We show that the universality class of the thermal transition is that of the d=2 classical spin model with the same symmetry. We provide evidence for the existence of a tricritical point in the (,temperature) plane. We also discuss numerical results by Hands et al. which showed that the system is critical for and the diquark condensate is zero.
The phase transition temperature for the Bose-Einstein condensation (BEC) of weakly-interacting Bose gases in three dimensions is known to be related to certain non-universal properties of the phase transition of three-dimensional O(2) symmetric theory. These properties have been measured previously in Monte Carlo lattice simulations. They have also been approximated analytically, with moderate success, by large approximations to O() symmetric theory. To begin investigating the region of validity of the large approximation in this application, I have applied the same Monte Carlo technique developed for the O(2) model ([5]) to O(1) and O(4) theories. My results indicate that there might exist some theoretically unanticipated systematic errors in the extrapolation of the continuum value from lattice Monte Carlo results. The final results show that the difference between simulations and NLO large calculations does not improve significantly from N=2 to N=4. This suggests one would need to simulate yet larger 's to see true large scaling of the difference. Quite unexpectedly (and presumably accidentally), my Monte Carlo result for N=1 seems to give the best agreement with the large approximation among the three cases.
We propose a multilevel Monte-Carlo scheme, applicable to local actions, which is expected to reduce statistical errors on correlation functions. We give general arguments to show how the efficiency and parameters of the algorithm are determined by the low-energy spectrum. As an application, we measure the euclidean-time correlation of pairs of Wilson loops in SU(3) pure gauge theory with constant relative errors. In this case the ratio of the new method's efficiency to the standard one increases as exp{m_0t/2}, where m_0 is the mass gap and t the time separation.
J. Engels🇩🇪 · L. Fromme🇩🇪 · M. Seniuch (Univ. Bielefeld)🇩🇪
We study an improved three-dimensional Ising model with external magnetic field near the critical point by Monte Carlo simulations. From our data we determine numerically the universal scaling functions of the magnetization, that is the equation of state, of the susceptibility and of the correlation length. In order to normalize the scaling functions we calculate the critical amplitudes of the three observables on the critical line, the phase boundary and the critical isochore. These amplitudes lead to the universal ratios C^+/C^-=4.756(28), R_{chi}=1.723(13), Q_c=0.326(3) and Q_2=1.201(10). We find excellent agreement of the data with the parametric representation of the asymptotic equation of state as found by field theory methods. The comparison of the susceptibility data to the corresponding scaling function shows a marginal difference in the symmetric phase, which can be explained by the slightly different value for R_{chi} used in the parametrization. The shape of the correlation-length-scaling function is similar to the one of the susceptibility, as expected from earlier parametrizations. The peak positions of the two scaling functions are coinciding within the error bars.
Stefano Arnone🇬🇧 · Antonio Gatti🇬🇧 · Tim R. Morris🇬🇧
We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The initial stages can even be computed diagrammatically. The method is formulated within the framework of an exact renormalization group for SU(N) Yang-Mills gauge theory, incorporating an effective cutoff through a manifest spontaneously broken SU(N|N) gauge invariance. We demonstrate the technique with a compact calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing, for the first time at finite N.
K. Langfeld🇩🇪 · J.C.R. Bloch🇩🇪 · A. Cucchieri🇧🇷 · J.Gattnar · T. Mendes🇧🇷 · H. Reinhardt🇩🇪
Simulations of SU(2) lattice gauge theory are used to establish a relation between the IR properties of Green functions and confinement. Using Landau gauge where the gauge configurations are restricted to the first Gribov regime, results on the ghost-, gluon form-factor and the running coupling constant are presented. Finally, we discuss the behavior of the ghost form-factor of the de-confined phase at high temperatures.
* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.