Abstract
The stationary points of the potential energy function of the ϕ^4 model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a globally-convergent Newton-Raphson method. We analyze the properties of the stationary points, in particular with respect to a number of quantities that have been conjectured to display signatures of the thermodynamic phase transition of the model. Although no such signatures are found for the nearest-neighbor ϕ^4 model, our study illustrates the strengths and weaknesses of the numerical methods employed.
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