Abstract
We present the results of a preliminary numerical study of a high dimensional periodic lattice version of classical ϕ4 theory. Using as a simple diagnostic for chaotic behaviour the rate of separation of neighbouring trajectories in phase space, we examine the existence of a stochasticity threshold that may vary with energy, initial conditions, lattice size, and the potential (single vs. double well). For an initial static gaussian, we find that the separation distance D(t) grows linearly for low energies and short times, corresponding to typical integrable behaviour, while log D(t) grows linearly for high energies, corresponding to chaotic behaviour. For moderate energies, we find that there can be a sudden onset of chaotic behaviour after long times. In the strongly chaotic cases, "saturation" is generally observed; i.e., log D reaches a maximum value at some t value and remains constant thereafter.
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