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Minimal potentials with very many minima

Solja&cbreve;ic1, Wilczek

  • 1Princeton University, Princeton, New Jersey 08544-1098, USA.

Physical Review Letters
|October 6, 2000
PubMed
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Simple matrix potentials with S(N) symmetry, unlike O(N) symmetry, can generate a vast number of distinct local minima. This finding is crucial for understanding complex energy landscapes in physics.

Area of Science:

  • Theoretical Physics
  • Mathematical Physics

Background:

  • Understanding the properties of matrix potentials is essential in various fields of physics.
  • Local minima in potential energy landscapes are critical for phenomena such as symmetry breaking and phase transitions.

Purpose of the Study:

  • To investigate the impact of symmetry groups on the number of local minima in renormalizable matrix potentials.
  • To demonstrate that S(N) symmetry leads to a significantly larger number of inequivalent local minima compared to O(N) symmetry.

Main Methods:

  • Construction of simple renormalizable matrix potentials.
  • Analysis of potentials with S(N) symmetry.
  • Comparison with potentials exhibiting O(N) symmetry.

Main Results:

Related Experiment Videos

  • Demonstrated that S(N) symmetric potentials can possess an exponentially large number of inequivalent deep local minima.
  • Showcased a constructive proof for this phenomenon.

Conclusions:

  • The choice of symmetry group (S(N) vs. O(N)) profoundly affects the complexity of the potential energy landscape.
  • This work provides a fundamental insight into the nature of local minima in theoretical models.