On the 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 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 v_c is actually non-coincident 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 phi^4 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.

10 pages, 9 figures, to appear in PRE

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Cited by in corpus (12)

• Phase transitions and configuration space topology
• The mean-field phi4-model: entropy, analyticity, and configuration space topology
• Energy landscape analysis of the two-dimensional nearest-neighbor ϕ^4 model
• Energy Landscape of the Finite-Size Mean-field 3-Spin Spherical Model
• Exploring the energy landscape of XY models
• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Topological Theory of Phase Transitions
• Mode-locking transitions in nano-structured weakly disordered lasers
• Phase transitions and topology in 2+k XY mean-field models
• When topology triggers a phase transition
• The topological hypothesis for discrete spin models
• Exact Topology of Dynamic Probability Surface of an Activated Process by Persistent Homology