Topology and phase transitions: From an exactly solvable model to a relation between topology and thermodynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 3, 2005, Pages

  Angelani, Luca ^a   Casetti, Lapo ^b   Pettini, Marco ^b,c   Ruocco, Giancarlo ^a   Zamponi, Francesco ^a  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

^c INAF OSSERVATORIO ASTROFISICO DI ARCETRI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CANONICAL ENSEMBLES (CE); PHASE SPACE; STATISTICAL PHYSICS; YANG-LEE THEORY;

ENTROPY; MATHEMATICAL TRANSFORMATIONS; PHASE TRANSITIONS; POTENTIAL ENERGY; ROTATION; TOPOLOGY; VECTORS;

THERMODYNAMICS;

EID: 41349112678     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.036152     Document Type: Article

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36. Mean-field models with long-range interactions, like those to be analyzed in the present paper, do not rigorously fulfill the hypotheses of the theorem proved in Ref. [8]; the fact that we do find a correspondence between the phase transition and a particular topology change also for these models, as already found in other models with long-range interactions, suggests that the theorem could be probably extended to a wider class of systems, which, however, would not necessarily include all the possible kinds of models with long-range, mean-fieldlike interactions (see also the discussion in Sec. IV).
37. This assumption is reasonable in the light of the results reported in Ref. [22].