Cutoff Effects Research Articles

Equation of state for two flavor QCD atNt=6

We calculate the two flavor equation of state for QCD on lattices with lattice spacing a = (6T) −1 and find that cutoff effects are substantially reduced compared to an earlier

Thermodynamics of the two-dimensional O(3) σ-model with fixed-point lattice action

The free energy density of the two-dimensional O(3) non-linear σ-model is calculated at finite temperature and finite spatial extent. Both an analytic calculation in the perturbative regime and a Monte Carlo study at low temperatures are presented. It is shown that using the fixed-point action instead of the standard Wilson action leads to a substantial reduction of the cut-off effects.

Thermodynamics of four-flavour QCD with improved staggered fermions

We have calculated the pressure and energy density in four-flavour QCD using improved fermion and gauge actions. We observe a strong reduction of finite cut-off effects in the high temperature regime, similar to what has been noted before for the SU(3) gauge theory. Calculations have been performed on 16 3 × 4 and 16 4 lattices for two values of the quark mass, ma = 0.05 and 0.1. A calculation of the string tension at zero temperature yields a critical temperature T c σ =0.407±0.010 for the smaller quark mass value.

Scaling topological charge in the CP 3 model using a fixed point action

We define a fixed point action in two-dimensional lattice CP N−1 models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cut-off effects in numerical simulations. Furthermore, the action has scale invariant instanton solutions, which enables us to define a topological charge without topological defects. We present results for the scaling of the topological suceptibility from a Monte Carlo simulation in the CP 3 model.

A look at lattice artifacts in weak matrix elements

Realistic estimates for systematic errors in weak matrix elements from the lattice are crucial for phenomenological applications. An important source of uncertainty is momentum dependent discretization errors. Pseudoscalar meson leptonic decays provide a good laboratory to explore momentum dependent cutoff effects.

QCD thermodynamics with improved actions

The thermodynamics of the SU(3) gauge theory has been analyzed with tree level and tadpole improved Symanzik actions. A comparison with the continuum extrapolated results for the standard Wilson action shows that improved actions lead to a drastic reduction of finite cut-off effects already on lattices with temporal extent N τ = 4. Results for the pressure, the critical temperature, surface tension and latent heat are presented. First results for the thermodynamics of four-flavour QCD with an improved staggered action are also presented. They indicate similarly large improvement factors for bulk thermodynamics.

SU(3) latent heat and surface tension from tree level and tadpole improved actions

We analyze the latent heat and surface tension at the SU(3) deconfinement phase transition with tree level and tadpole improved Symanzik actions on lattices with temporal extent N τ = 3 and 4 and spatial extent N σ N τ = 4, 6 and 8 . In comparison to the standard Wilson action we do find a drastic reduction of cut-off effects already with tree level improved actions. On lattices with temporal extent N τ = 4 results for the surface tension and latent heat obtained with a tree level improved action agree well with those obtained with a tadpole improved action. A comparison with N τ = 3 calculations, however, shows that results obtained with tadpole action remain unaffected by cut-off effects even on this coarse lattice, while the tree level action becomes sensitive to the cut-off. For the surface tension and latent heat we find σ 1 T c 3 = 0.0155 (16) and Δϵ T c 4 = 1.40 (9), respectively.

Mass bounds in a Z 2 scalar-fermion model

The lattice regularized Z2 scalar-fermion model using staggered fermions in four dimensions is investigated in the broken symmetry phase. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type of Yukawa interaction. Triviality upper bound and vacuum stability lower bound on the mass of the scalar particle are numerically estimated. Qualitative agreement between Monte Carlo data and one-loop perturbative results is obtained. Systematic errors of the upper bound are estimated. At strong Yukawa coupling, we see some quantitative disagreements due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.

SU(3) thermodynamics on small lattices

The free energy density of the SU(3) gauge theory at temperatures T/ T c = 4/3, 3/2 and 2 is calculated on lattices with temporal extent as small as N τ = 2,3 and spatial extent N δ = 4 N τ using parametrized fixed point actions. Although cut-off effects are seen, they are hugely suppressed with respect to Wilson and Symanzik-improved actions and at N τ = 3 there is already a good agreement with the continuum limit as extrapolated from the results with the Wilson action at N τ = 6 and 8.

Chiral symmetry and O( a) improvement in lattice QCD

The dominant cutoff effects in lattice QCD with Wilson quarks are proportional to the lattice spacing a. In particular, the isovector axial current satisfies the PCAC relation only up to such effects. Following a suggestion of Symanzik, they can be cancelled by adding local O( a) correction terms to the action and the axial current. We here address a number of theoretical issues in connection with the O( a) improvement of lattice QCD and then show that chiral symmetry can be used to fix the coefficients multiplying the correction terms.

Fixed point action and topology in the CP3 model.

We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$ models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cutoff effects in numerical simulations. Furthermore, the action has scale-invariant instanton solutions, which enables us to define a correct topological charge without topological defects. Using a parametrization of the fixed point action for the ${\rm CP}^{3}$ model in a Monte Carlo simulation, we study the topological susceptibility.

Cut-off effects in biological activities of surfactants

In the homologous series of long hydrocarbon chain surface active compounds, their various biological activities increase progressively with increasing chain length up to a critical point, beyond which the compounds cease to be active. The paper reviews several hypotheses of this cut-off effect in biological activities and experimental evidences supporting them. It is suggested that the lateral expansion of the phospholipid bilayer of biological membranes caused by the intercalation of long-chain amphiphile molecules between the phospholipid molecules and the mismatch between their hydrocarbon chain lengths results in the creation of free volume in the bilayer hydrophobic region. The elimination of the free volume via the hydrocarbon chain trans-gauche isomerisation or interdigitation results in the bilayer thickness change or in its destabilisation and formation of non-bilayer phase(s). In combination with the partition and ionisation equilibria of amphiphiles in the lipid/aqueous phase systems, the free volume predicts similar chain length and pH dependencies as observed in biological experiments. It is suggested that the free volume mechanism, in combination with other mechanisms, could be responsible for the cut-off effects in biological activities of amphiphiles.

Equation of state in the quark-gluon plasma

Results from quenched simulations of QCD at finite temperature are presented. We calculated pressure and energy density. With the standard Wilson action we worked on several large lattices, with temporal extent Nτ = 4, 6 and 8 and spatial extent Nσ = 16 and 32. This enables to control finite lattice spacing effects and to extrapolate the results to the continuum limit. We find a deviation from ideal gas behaviour of about 15%, even at temperatures as high as T ∼ 5Tc. A calculation of the critical temperature on lattices with temporal extent Nτ = 8 and 12 and the string tension on 324 lattices at the corresponding critical couplings is performed to fix the temperature scale. An extrapolation to the continuum limit yields Tc/√σ = 0.629(3). These results are then compared to simulations with improved lattice actions. We can demonstrate that at high temperatures the cut-off effects can be reduced considerably.

Improved actions for QCD thermodynamics on the lattice

Finite cut-off effects strongly influence the thermodynamics of lattice regularized QCD at high temperature in the standard Wilson formulation. We analyze the reduction of finite cut-off effects in formulations of the thermodynamics of SU(N) gauge theories with three different O( a 2) and O( a 2) improved actions. We calculate the energy density and pressure on finite lattices in leading order weak coupling perturbation theory ( T → ∞) and perform Monte Carlo simulations with improved SU(3) actions at non-zero g 2. Already on lattices with temporal extent N τ = 4 we find a strong reduction of finite cut-off effects in the high temperature limit, which persists also down to temperatures a few times the deconfinement transition temperature.

Bounds on the renormalized couplings in a Z2 Scalar-Fermion model

The triviality upper bound and the vacuum stability lower bound on the mass of the scalar particle is numerically investigated in a Z2 scalar-fermion model using staggered fermions. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type Yukawa interaction. Reasonable agreement between Monte Carlo data and one-loop perturbative results is obtained except that at strong Yukawa couplings, significant deviations arise due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.

Desperately seeking chiral fermions

Chiral fermions can (presumably) be constructed by introducing two regulators, one for the gauge fields (e.g. a lattice), and another for the fermion functional integrals in a fixed (regulated) gauge field. This talk discusses cutoff effects arising from the regulator of the fermions.

Membrane Fouling and Molecular Weight Cutoff Effects on the Partitioning of Pectinesterase

The effects of membrane fouling and molecular weight cutoff (MWCO) on the partitioning of pectinesterase (PE) isolated from Marsh grapefruit were evaluated. Statistically higher fouling rates were observed for Marsh grapefruit extracts on 30K and 100K poly(sulfone) UF membranes than on a similar membrane with a MWCO of 10K. A simple logarithmic expression adequately described the fouling phenomena for all three UF membranes. The permeability of PE was also determined by using the same membranes and found to decrease 30−60% during processing regardless of the MWCO of the membrane. Permeability was found to decrease in a fashion similar to permeate flux. A separate logarithmic expression was developed to evaluate the rate of change of permeability on each of the membranes. About 40−50% of the total activity in the permeate of the 30K UF membrane was thermostable PE. Keywords: Polysulfone membrane; thermostable pectinesterase; citrus processing

Fixed point actions for SU(3) gauge theory

We summarize our recent work on the construction and properties of fixed point (FP) actions for lattice SU(3) pure gauge theory. These actions have scale invariant instanton solutions and their spectrum is exact through 1-loop, i.e. in their physical predictions there are no a n nor g 2 a n cut-off effects for any n. We present a few-parameter approximation to a classical FP action which is valid for short correlation lengths. We perform a scaling test of the action by computing the quantity G=L σ(L) , where the string tension σ( L) is measured from the torelon mass μ = Lσ( L), on lattices of fixed physical volume and varying lattice spacing a. While the Wilson action shows scaling violations of about ten per cent, the approximate fixed point action scales within the statistical errors for 1 2 ≥ aT c .

Equation of State for the SU(3) Gauge Theory.

Through a detailed investigation of the $SU(3)$ gauge theory at finite temperature on lattices of various size we can control finite lattice cut-off effects in bulk thermodynamic quantities. We calculate the pressure and energy density of the $SU(3)$ gauge theory on lattices with temporal extent $N_\tau = 4$, 6 and 8 and spatial extent $N_\sigma =16$ and 32. The results are extrapolated to the continuum limit. We find a deviation from ideal gas behaviour of (15-20)\%, depending on the quantity, even at temperatures as high as $T\sim 3T_c$. A calculation of the critical temperature on lattices with temporal extent $N_\tau = 8$ and 12 and the string tension on $32^4$ lattices at the corresponding critical couplings is performed to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrt{\sigma} = 0.629(3)$.

The classically perfect fixed-point action for SU(3) gauge theory

In this paper (the first of a series) we describe the construction of fixed-point actions for lattice SU(3) pure gauge theory. Fixed-point actions have scale-invariant instanton solutions and the spectrum of their quadratic part is exact (they are classical perfect actions). We argue that the fixed-point action is even one-loop quantum perfect, i.e. in its physical predictions there are no g 2 a n cut-off effects for any n. We discuss the construction of fixed-point operators and present examples. The lowest-order q q potential V( r) obtained from the fixed-point Polyakov loop correlator is free of any cut-off effects which go to zero as an inverse power of the distance r.