title: Energy-landscape analysis of the two-dimensional nearest-neighbor φ⁴ model.
abstract: The stationary points of the potential energy function of the φ⁴ 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 φ⁴ model, our study illustrates the strengths and weaknesses of the numerical methods employed.
authors.affiliation: Department of Physics, Syracuse University, Syracuse, New York 13244, USA. dbmehta@syr.edu
authors.forename: Dhagash
authors.initials: D
authors.lastname: Mehta
authors.forename: Jonathan D
authors.initials: JD
authors.lastname: Hauenstein
authors.forename: Michael
authors.initials: M
authors.lastname: Kastner
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D008956:Models, Chemical; D009716:Numerical Analysis, Computer-Assisted; D013816:Thermodynamics