We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the ±1 Ising model with nearest neighbour and body diagonal interaction, the spin-1 model with states 0, ±1, and nearest neighbour interaction, and φ 4 -theory on the lattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling properties of the suitably tuned spin-1 model are compared in detail with those of the standard Ising model. Great care is taken to estimate the systematic errors from residual corrections to scaling. Our best estimates for the critical exponents are ν = 0.6298(5) and η = 0.0366(8), where the given error estimates take into account the statistical and systematic uncertainties.

In the confining phase of any gauge system the mean squared width of the colour flux tube joining a pair of quarks should grow logarithmically as a function of their distance, according to the effective string description of its infrared properties. New data on 3D Z Z 2 gauge theory, combined with high precision data on the interface physics of the 3D Ising model fit nicely this behaviour over a range of more than two orders of magnitude.

No abstract

We describe a high precision Monte Carlo test on Z2 and Z5 gauge models in 3D. Wilson loops of size 2≤R, T≤12 are measured and values of the string tension σ are extracted. These values fulfil asymptotic scaling if and only if the string contributions, namely the quantum fluctuations of the surfaces bordered by Wilson loops, are properly taken into account. As a byproduct of our analysis we find the signature of the finite thickness of these flux tubes.

The interface between domains of opposite magnetization in the 3D Ising model near the critical temperature displays universal finite-size effects which can be described in terms of a gaussian model of capillary waves. It turns out that these finitesize corrections depend rather strongly on the shape of the lattice. This prediction, which has no adjustable parameters, is tested and accurately verified for various lattice shapes by means of numerical simulations with a cluster algorithm. This supports also a long-standing conjecture on the finite-size effects in Wilson loops of Lattice Gauge Theories.