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 non-confining 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 vc is actually non-coincident with, and always higher than, the energy vθ at which a topological change appears. However, applying a procedure already successfully employed in other cases as the mean field φ 4 model, i. e. introducing a map M: v → vs from levels of the energy hypersurface V to the level of the stationary points ”visited” at temperature T , we find that M(vc)=vθ. 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.

Relationship between phase transitions and topological changes in one-dimensional models / Angelani, L.; Ruocco, G.; Zamponi, F.. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 72:(2005), p. 016122. [10.1103/PhysRevE.72.016122]

Relationship between phase transitions and topological changes in one-dimensional models

L. ANGELANI;G. RUOCCO;F. ZAMPONI
2005

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 non-confining 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 vc is actually non-coincident with, and always higher than, the energy vθ at which a topological change appears. However, applying a procedure already successfully employed in other cases as the mean field φ 4 model, i. e. introducing a map M: v → vs from levels of the energy hypersurface V to the level of the stationary points ”visited” at temperature T , we find that M(vc)=vθ. 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.
2005
Topology; phase transitions; statistical mechanics
01 Pubblicazione su rivista::01a Articolo in rivista
Relationship between phase transitions and topological changes in one-dimensional models / Angelani, L.; Ruocco, G.; Zamponi, F.. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 72:(2005), p. 016122. [10.1103/PhysRevE.72.016122]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/81939
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