Towards the goal of extracting the continuum properties, we have studied the Topological Charge Density Correlator (TCDC) and the Inverse Participation Ratio (IPR) for the topological charge density (q(x)) in SU(3) Lattice Yang-Mills theory for relatively small lattice spacings including some smaller than those explored before. With the help of recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since trapping problem is absent. On the other hand, the reference energy scale provided by Wilson flow allows us to study their scaling behavior in contrast to previously proposed smearing techniques. The behavior of TCDC for different lattice spacings at a fixed HYP smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time t for all the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of TCDC are studied by investigating the small flow time behavior. We have also extracted the pseudoscalar glueball mass from TCDC, which appears to be insensitive to the lattice spacings (0.0345 fm ≤ a ≤ 0.0667 fm) and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we have studied the localization property of q(x) through IPR whose continuum behavior can be probed through the small values of Wilson flow time and observed the decrease of IPR with decreasing Wilson flow time. A detailed study of q(x) under Wilson flow time revealed that as Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitudes increases, and the charge density appears to be more delocalized resulting in the observed behavior of IPR.

We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.

Using non-perturbative lattice method we studied hadronic screening correlators above and immediately below the deconfinement transition temperature, Tc, in the quenched approximation with lattice spacing of 1/(8T) using clover improved Wilson fermions. Simulations were performed at temperatures T /Tc = 0, 0.95 and 1.5. Mesonic screening correlators show no statistically significant thermal effects below Tc, and clear evidence for weakly interacting quarks above Tc . Baryon screening correlators yield similar physics above Tc, but show precursor effects for chiral symmetry restoration below Tc .Comment: 12 pages, 8 figures, typos correcte

A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV ≤ 1 a ≤ 5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV ≤ 1 a ≤ 5.7 GeV.

In this work we perform a detailed numerical analysis of (1+1) dimensional lattice φ 4 theory. We explore the phase diagram of the theory with two different parameterizations. We find that symmetry breaking occurs only with a negative mass-squared term in the Hamiltonian. The renormalized mass m R and the field renormalization constant Z are calculated from both coordinate space and momentum space propagators in the broken symmetry phase. The critical coupling for the phase transition and the critical exponents associated with m R , Z and the order parameter are extracted using a finite size scaling analysis of the data for several volumes. The scaling behavior of Z has the interesting consequence that φ R does not scale in 1 + 1 dimensions. We also calculate the renormalized coupling constant λ R in the broken symmetry phase.The ratio λ R /m 2 R does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.