Numerical methods are used to investigate some of the non-perturbative properties of lattice QCD. With the aid of Monte Carlo techniques based on the canonical ensemble, we calculate the QCD potential between a pair of heavy quarks, in the quenched approximation (no dynamical quarks). We find that the potential exhibits a linear dependence on distance at distances of the order of a fermi, which is consistent with the expected confining property of QCD. At smaller distances, we observe that the potential follows a 1/R type behaviour. We also compute the mass of the 0++ glueball for the SU(3) gauge group. We implement several statistical improvements in this calculation, in order to extract the mass reliably from the Monte Carlo simulations. We obtain a mass value of ≈1400 MeV for this glue ball state (in the quenched approximation).
Finally, we use a numerical method, called the "demon" method, which is based upon the microcanonical ensemble, to measure the flow of lattice actions for the group SU(2) under renormalisation transformations generated by the Monte Carlo Renormalisation Group technique. We find that the demon method is ideally suited to the problem of tracking these renormalisation flows. Using the method, we arc able to obtain an "improved" lattice action, which better describes physics near the continuum limit than the more straightforward naive actions.
