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Related Experiment Videos

Topology, phase transitions, and the spherical model.

Sebastián Risau-Gusman1, Ana C Ribeiro-Teixeira, Daniel A Stariolo

  • 1Departamento de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970, Porto Alegre, Brazil. srisau@cab.cnea.gov.ar

Physical Review Letters
|October 26, 2005
PubMed
Summary

Topological changes in configuration space are not always sufficient to indicate phase transitions. This study shows discontinuities in topological functions do not align with phase transitions in the Berlin-Kac spherical model.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Topology

Background:

  • The topological hypothesis posits a link between phase transitions and configuration space topology.
  • Previous work established the necessity of topological changes for phase transitions.

Purpose of the Study:

  • To precisely characterize the configuration space topology of the short-range Berlin-Kac spherical model.
  • To investigate the relationship between topological changes and phase transitions in this model for varying dimensions (d).

Main Methods:

  • Analysis of the configuration space topology for the Berlin-Kac spherical model on hypercubic lattices.
  • Examination of topological functions and their discontinuities in relation to phase transitions.

Main Results:

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  • A continuum of topological changes was observed.
  • A finite number of discontinuities in topological functions were identified.
  • These topological discontinuities were shown to not coincide with phase transitions for d >= 3.

Conclusions:

  • The study demonstrates that topological changes are not always sufficient to predict phase transitions.
  • This is the first short-range confining potential model where topological changes do not guarantee a phase transition.