LATTICE-FREE SIMULATIONS OF TOPOLOGICAL DEFECT FORMATION - ART. NO. 103501

We examine simulations of the formation of domain walls, cosmic string s, and monopoles on a cubic lattice, in which the topological defects are assumed to lie at the zeros of a piecewise constant 1, 2, or 3 com ponent Gaussian random field, respectively. We derive analytic express ions for the corresponding topological defect densities in the continu um limit and show that they fail to agree with simulation results, eve n when the fields are smoothed on small scales to eliminate lattice ef fects. We demonstrate that this discrepancy, which is related to a cla ssic geometric fallacy, is due to the anisotropy of the cubic lattice, which cannot be eliminated by smoothing. This problem can be resolved by linearly interpolating the field values on the lattice, which give s results in good agreement with the continuum predictions. We use thi s procedure to obtain a lattice-free estimate (for Gaussian smoothing) of the fraction of the total length of string in the form of infinite strings: f(infinity) = 0.716+/-0.015. [S0556-2821(98)03122-1].