Topological Signature of First Order Phase Transitions

Details Topological Signature of First Order Phase Transitions Topological Signature of First Order Phase Transitions

2002-05-23

arxiv.org/abs/cond-mat/0205483v1

Europhys. Lett. 62, 775 (2003)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 2 figures

Scientific paper

10.1209/epl/i2003-00439-9

We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In particular, we present the thermodynamics of an analytically solvable mean-field model with a k-body interaction which -depending on the value of k- displays no transition (k=1), second order (k=2) or first order (k>2) phase transition. This rich behavior is quantitatively retrieved by the investigation of a topological invariant, the Euler characteristic, of some submanifolds of the configuration space. Finally, we conjecture a direct link between the Euler characteristic and the thermodynamic entropy.

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