Topology and phase transitions: Paradigmatic evidence

Physical Review Letters

Volumn 84, Issue 13, 2000, Pages

  Franzosi, Roberta ^a,c,e   Pettini, Marco ^b,c,f   Spinelli, Lionel ^c,d  

^a UNIVERSITY OF FLORENCE   (Italy)

^b INAF OSSERVATORIO ASTROFISICO DI ARCETRI   (Italy)

^c INFM   (Italy)

^d CENTRE DE PHYSIQUE THÉORIQUE   (France)

^e POLITECNICO DI TORINO   (Italy)

^f Sezione di Firenze   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EIFFEOMORPHISM INVARIANTS; EULER CHARACTERISTICS; PARTITION FUNCTIONS; TOPOLOGIC INVARIANTS;

FUNCTIONS; HAMILTONIANS; PHASE TRANSITIONS; POTENTIAL ENERGY; THEOREM PROVING; THERMODYNAMICS; TOPOLOGY; VECTORS;

POLYMERS;

EID: 4243588056     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.84.2774     Document Type: Article

References (17)

1. Discrete variables systems, like spin systems, require a much more abstract context to relate phase transitions with topology changes; suitable vector bundles must be considered; see M. Rasetti, in Typological Concepts in Phase Transition Theory, edited by H. D. Dö bner, Differential Geometric Methods in Mathematical Physics (Springer, New York, 1979).
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6. A diffeomorphism is a one-to-one differentiable application with differentiable inverse.
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11. M. Spivak, Comprehensive Introduction to Differential Geometry (Publish or Perish, Berkeley, 1979), Vol. V, Chap. 13.
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14. We borrowed from statistical mechanics the Metropolis' recipe to construct a Markov process that samples a given Lebesgue measure [see K. Binder, Monte Carlo Methods in Physics (Springer-Verlag, New York, 1979)]. However our Monte Carlo simulations have nothing to do with those of numerical statistical mechanics.
15. ν) written using a geometric derivation formula in Ref. [2].
16. ν can be of any kind; there are manifolds whose Betti numbers (in terms of which χ is defined) are factorially growing with N, others - like hyperspheres - for which χ is a constant independent of N.
17. L. Caiani, L. Casetti, and M. Pettini, J. Phys. A 31, 3357 (1998).