title: Relationship between phase transitions and topological changes in one-dimensional models.
abstract: We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model and the Peyrard-Bishop model for DNA thermal denaturation, both in the confining and nonconfining version. These models, apparently, do not fit [M. Kastner, Phys. Rev. Lett. 93, 150601 (2004)] in the general idea that the phase transition is signaled by a topological discontinuity. We show that in both models the phase transition energy v(c) is actually noncoincident with, and always higher than, the energy v(theta) at which a topological change appears. However, applying a procedure already successfully employed in other cases as the mean field phi4 model, i.e., introducing a map M:v-->v(s) from levels of the energy hypersurface V to the level of the stationary points "visited" at temperature T, we find that M (v(c))=v(theta). This result enhances the relevance of the underlying stationary points in determining the thermodynamics of a system, and extends the validity of the topological approach to the study of phase transition to the elusive one-dimensional systems considered here.
authors.affiliation: Dipartimento di Fisica, Università di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy.
authors.forename: L
authors.initials: L
authors.lastname: Angelani
authors.forename: G
authors.initials: G
authors.lastname: Ruocco
authors.forename: F
authors.initials: F
authors.lastname: Zamponi
mesh_terms: D001703:Biophysics / Q000379:methods*; D004247:DNA / Q000737:chemistry*; D015233:Models, Statistical; D009690:Nucleic Acid Conformation; D044367:Phase Transition; D013499:Surface Properties; D013696:Temperature; D013816:Thermodynamics
chemical_list: D004247:DNA