2011/08/31 by Michael Kästner, Michael Kastner, Dhagash Mehta · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Energy (signal processing) #Energy landscape #Mathematics #Phase (matter) #Phase Equilibria and Thermodynamics #Phase transition #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Stationary point #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.107.160602
published as Phys. Rev. Lett. 107, 160602 (2011) · 5 pages, 3 figures
arxiv created 2011/10/13 · openalex publication_date 2011/10/13 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The stationary points of the potential energy function V are studied for the ϕ4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of stationary points to the occurrence of thermodynamic phase transitions. We find that the phase transition potential energy of the ϕ4 model does in general not coincide with the potential energy of any of the stationary points of V. This disproves earlier, allegedly rigorous, claims in the literature on necessary conditions for the existence of phase transitions. Moreover, we find evidence that the indices of stationary points scale extensively with the system size, and therefore the index density can be used to characterize features of the energy landscape in the infinite-system limit. We conclude that the finite-system stationary points provide one possible mechanism of how a phase transition can arise, but not the only one.