Dhagash Mehta, Michael Kastner, Jonathan D. Hauenstein
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.
View original:
http://arxiv.org/abs/1202.3320
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