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We present an analytical continuum calculation, starting from first principles, of the vacuum wavefunction and string tension for pure Yang-Mills theories in $(2+1)$ dimensions, extending our previous analysis using gauge-invariant matrix variables. The vacuum wavefunction is consistent with what is expected at both high and low momentum regimes. The value of the string tension is in very good agreement with recent lattice Monte Carlo evaluations., 12 pages, plainTex, some clarifying remarks and one reference added

We study the coefficients of the expansion $F(R) = 1/3 c_3 R^3 + 1/2 c_2 R^2 + c_1 R$ of the free energy of spherical bubbles at $T=T_c$ in pure glue QCD using lattice Monte Carlo techniques. The coefficient $c_3$ vanishes at $T=T_c$ and our results suggest that the sign and the order of magnitude of $c_1$ is in agreement with the value $c_1=\pm 32\pi T_c^2/9$ (- for hadronic bubbles in quark phase, + for quark bubbles in hadronic phase) computed by Mardor and Svetitsky from the MIT bag model. The parameter $c_2$ is small in agreement with earlier determinations., Comment: (11 pages; 10 ps-figures)

In statistical systems with a first-order phase transition, for example, in hot QCD matter, the ordered and disordered phases can coexist at T c with an interface in between. We study a lattice Monte Carlo method for determing the tension of the interface by applying the method to a particularly simple model, the 7-state Potts model in two dimensions. The method shows very clearly also the structure of the interface.

We have measured the mass gap in pure SU(2) gauge theory with Manton's action by means of our previously proposed long distance correlation method. Asymptotic freedom is verified over the β-range 1.3 ⩽ β ⩽ 1.8. The ratio between the lowest glueball mass and the square root of the string tension extracted from lattice calculations is shown to be universal, i.e. it is the same for Manton's and Wilson's action.

It is pointed out that the usual bag model explanation of the linear heavy quark potential is in conflict with lattice Monte Carlo results for the string tension in the adjoint (and higher) representations. The discrepancy is due to an insufficient “collimation” of the electric flux lines for strong color sources. An alternative model for the formation of flux tubes is discussed.

The massive Schwinger model with two flavours is studied using the local hamiltonian lattice Monte Carlo method. Chiral symmetry breaking is studied using the fermion condensate as order parameter. For a small ratio of the two fermion masses, degeneracy of the two flavours is found. For a large ratio of the masses, the heavy flavour decouples and the light fermion behaves like in the one flavour Schwinger model.

We have calculated the glueball masses of various spins and parities in SU(3) gauge theory. Our first results give m M (0 ++ )=(3.6±0.2) Λ mom , m E (0 ++ )=(4.3±0.3) Λ mom , m (0 −+ )=(7.2 −0.9 +1.6 ) Λ mom , m M (2 ++ )=(8.1±1.1) Λ mom and m E (2 ++ )=(8.3 −1.0 +1.6 ) Λ mom as well as information on the glueball wave functions.