B. Bonnier

On the random filling of Rd by non-overlapping d-dimensional cubes

Abstract We compute the time-dependent coverage in the random sequential adsorption of aligned d-dimensional cubes in R d using time-series expansions. The seventh-order series in 2,3 and 4 dimensions is resummed in order to predict the coverage at jamming. The result is in agreement with Monte Carlo simulations. A simple argument, based on a property of the pertubative expansion valid at arbitrary orders, allows us to analytically derive some generalizations of the Palasti approximation.

On the strong coupling expansion of the Φd2k theory

Abstract The strong coupling expansion of the Φ2k field theory with either usual or gaussian propagators is investigated in a d-dimensional euclidean space. Some simple diagrams which occur at all orders of the vacuum energy density expansion are summed. This resummation is shown to give, in the zero lattice spacing limit, good results for all anharmonic oscillators, even for k = ∞, and in all dimensions in the case of a gaussian propagator.

On the critical behaviour of Φd2k from the massive continuum limit of the Ising model

Abstract The continuum limit of the first four renormalized vertices of the Ising model are derived from a large order strong coupling expansion in the regime in which the bare coupling is infinite and the renormalized mass held fixed. This method of computing the critical superpotential of Φ d 2 k is discussed for the euclidean dimension d . In one dimension, exact results can be obtained analytically, and the method remains perfectly reliable up to d = 2. Its validity is, however, unclear at higher dimension, for which we present some conjectures.

Langevin simulation of the ising model with application to field theory in two and three dimensions

A Langevin method is developed for computing the spin correlations of the Ising model. It is applied in two and three dimensions in order to evaluate critical quantities, including the renormalized coupling constant of the corresponding field theory. A simple minimization of finite size effects is shown to give a realistic determination of these numbers from quite small lattices.

A large-order analysis of one-dimensional lattice strong coupling expansions

Abstract A large order lattice strong coupling expansion for the ground state energy of the quantum mechanical hamiltonian 1 2 p 2 + g|x| α , α > 0 , is provided by a perturbative solution of the transfer matrix eigenvalue equation. This algorithmic derivation allows one to perform either an analytic or a very large order ( N ∼ 50) numerical study of the expansion, which in particular is found to have a finite radius of convergence for α ⩾ 2. These results, which can be useful for a better understanding of this model when treated as a quantum field theory, indicate that the continuum limit can be safely extracted but that the rate of convergence is generally very poor.

Continuous regularizations in strong coupling expansions from a generalized inverse propagator method

A strong coupling expansion is derived in terms of a generalized inverse propagator and is used to construct a regularization scheme which, for some regulators, differs from the canonical one. In particular, the Gaussian cut-off is shown to induce unbiased results, in contrast to a previous analysis using this regulator in the standard way. Several continuous and discrete regulations are then compared through a numerical example which suggests their equivalence.