Energy landscape analysis of the two-dimensional nearest-neighbor φ^4 model

Details Energy landscape analysis of the two-dimensional nearest-neighbor φ^4 model Energy landscape analysis of the two-dimensional nearest-neighbor φ^4 model

2012-02-15

arxiv.org/abs/1202.3320v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 6 figures

Scientific paper

The stationary points of the potential energy function of the \phi^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 \phi^4 model, our study illustrates the strengths and weaknesses of the numerical methods employed.

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