Speeding up finite step-size updating of full QCD on the lattice

We propose various improvements of finite step-size updating for full QCD on the lattice that might turn finite step-size updating into a viable alternative to the hybrid Monte Carlo algorithm. These improvements are noise reduction of the noisy estimator of the fermion determinant, unbiased inclusion of the hopping parameter expansion and a multi-level Metropolis scheme. First numerical tests are performed for the 2 dimensional Schwinger model with two flavours of Wilson fermions and for QCD two flavours of Wilson fermions and Schr"odinger functional boundary conditions.Comment: 22 pages, 1 figur

Spin susceptibility of the superfluid 3^{3}He-B in aerogel

The temperature dependence of paramagnetic susceptibility of the superfluid ^{3}He-B in aerogel is found. Calculations have been performed for an arbitrary phase shift of s-wave scattering in the framework of BCS weak coupling theory and the simplest model of aerogel as an aggregate of homogeneously distributed ordinary impurities. Both limiting cases of the Born and unitary scattering can be easily obtained from the general result. The existence of gapless superfluidity starting at the critical impurity concentration depending on the value of the scattering phase has been demonstrated. While larger than in the bulk liquid the calculated susceptibility of the B-phase in aerogel proves to be conspicuously smaller than that determined experimentally in the high pressure region.Comment: 10 pages, 4 figures, REVTe

Universal Behaviour of the Superfluid Fraction and Tc of He-3 in 99.5% Open Aerogel

We have investigated the superfluid transition of He-3 in a 99.5% porosity silica aerogel. This very dilute sample shows behaviour intermediary between bulk He-3 and He-3 confined to the denser aerogels previously studied. We present data on both the superfluid transition temperature and the superfluid density and compare our results with previous measurements. Finally, we show that the suppression of the superfluid transition temperature and suppression of the superfluid density of He-3 in aerogel follow a universal relation for a range of aerogel samples.Comment: 4 pages, 5 figures; 1 new figure, minor change

Cooling and the SU(2) Instanton Vaccuum

We present results of an investigation into the nature of instantons in 4-dimensional pure gauge lattice $SU(2)$\ obtained from configurations which have been cooled using an under-relaxed cooling algorithm. We discuss ways of calibrating the cooling and the effects of different degrees of cooling, and compare our data for the shapes, sizes and locations of instantons with continuum results. In this paper we extend the ideas and techniques developed by us for use in $O(3)$, and compare the results with those obtained by other groups.Comment: 22 pages, LaTeX, uuencoded compressed tarfile of figures sent separately. Full (compressed) postscript version (118k)available from ftp://rock.helsinki.fi/pub/preprints/tft/Year1995/HU-TFT-95-21/paper.ps.

Influence of the U(1)_A Anomaly on the QCD Phase Transition

The SU(3)_{r} \times SU(3)_{\ell} linear sigma model is used to study the chiral symmetry restoring phase transition of QCD at nonzero temperature. The line of second order phase transitions separating the first order and smooth crossover regions is located in the plane of the strange and nonstrange quark masses. It is found that if the U(1)_{A} symmetry is explicitly broken by the U(1)_{A} anomaly then there is a smooth crossover to the chirally symmetric phase for physical values of the quark masses. If the U(1)_{A} anomaly is absent, then there is a phase transition provided that the \sigma meson mass is at least 600 MeV. In both cases, the region of first order phase transitions in the quark mass plane is enlarged as the mass of the \sigma meson is increased.Comment: 5 pages, 3 figures, Revtex, discussion extended and references added. To appear in PR

Instantons and Chiral Symmetry on the Lattice

I address the question of how much of QCD in the chiral limit is reproduced by instantons. After reconstructing the instanton content of smoothed Monte Carlo lattice configurations, I compare hadron spectroscopy on this instanton ensemble to the spectroscopy on the original ``physical'' smoothed configurations using a chirally optimised clover fermion action. By studying the zero mode zone in simple instances I find that the optimised action gives a satisfactory description of it. Through the Banks-Casher formula, instantons by themselves are shown to break chiral symmetry but hadron correlators on the instanton backgrounds are strongly influenced by free quark propagation. This results in unnaturally light hadrons and a small splitting between the vector and the pseudoscalar meson channels. Superimposing a perturbative ensemble of zero momentum gauge field fluctuations (torons) on the instantons is found to be enough to eliminate the free quarks and restore the physical hadron correlators. I argue that the torons that are present only in finite volumes, are probably needed to compensate the unnaturally large finite size effects due to the lack of confinement in the instanton ensemble.Comment: 32 pages, LaTeX with 14 eps figure

Model of Inhomogeneous Impurity Distribution in Fermi Superfluids

The standard treatment of impurities in metals assumes a homogeneous distribution of impurities. In this paper we study distributions that are inhomogeneous. We discuss in detail the "isotropic inhomogeneous scattering model" which takes into account the spatially varying scattering on the scale of the superfluid coherence length. On a large scale the model reduces to a homogeneous medium with renormalized parameter values. We apply the model to superfluid 3He, where porous aerogel acts as the impurity. We calculate the transition temperature Tc, the order parameter, and the superfluid density. Both A- and B-like phases are considered. Two different types of behavior are identified for the temperature dependence of the order parameter. We compare the calculations with experiments on 3He in aerogel. We find that most of the differences between experiments and the homogeneous theory can be explained by the inhomogeneous model. All our calculations are based on the quasiclassical theory of Fermi liquids. The parameters of this theory for superfluid 3He in aerogel are discussed.Comment: 14 pages, 9 figures, minor change

Effects of non-perturbatively improved dynamical fermions in QCD at fixed lattice spacing

We present results for the static inter-quark potential, lightest glueballs, light hadron spectrum and topological susceptibility using a non-perturbatively improved action on a $16^3\times 32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units ($\sim 1.7$ fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavours of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ($M_{PS}/M_{V}\ge0.58$). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.Comment: 53 pages, LaTeX/RevTeX, 16 eps figures; corrected clover action expression and various typos, no results change