2004/05/10 by A. Andronico, Luca Angelani, L. Angelani +4 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Energy (signal processing) #Field (mathematics) #Geometry #Material Dynamics and Properties #Mathematics #Phase transition #Physics #Quantum mechanics #Saddle point #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #Thermodynamics #Topology (electrical circuits) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.70.041101
published as Phys.Rev. E70 (2004) 041101 · 14 pages, 9 figures
arxiv created 2004/05/10 · openalex publication_date 2004/10/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the thermodynamics and the properties of the stationary points (saddles and minima) of the potential energy for a phi4 mean-field model. We compare the critical energy vc [i.e., the potential energy vT evaluated at the phase transition temperature Tc ] with the energy vtheta at which the saddle energy distribution show a discontinuity in its derivative. We find that, in this model, vc >> vtheta, at variance to what has been found in different mean-field and short ranged systems, where the thermodynamic phase transitions take place at vc=vtheta [Phys. Rep. 337, 237 (2000)]]. By direct calculation of the energy vs T of the "inherent saddles," i.e., the saddles visited by the equilibrated system at temperature T , we find that vsTc approximately vtheta. Thus, we argue that the thermodynamic phase transition is related to a change in the properties of the inherent saddles rather than to a change of the topology of the potential energy surface at T= Tc. Finally, we discuss the approximation involved in our analysis and the generality of our method.