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This study proves that two-dimensional hard-core particle models with Vicsek-type interactions do not break rotational symmetry at any temperature. This finding challenges the idea that particle mobility causes symmetry breaking in such models.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • Vicsek-type models describe self-propelled particles with alignment interactions.
  • Spontaneous symmetry breaking is a key phenomenon in statistical mechanics.
  • Previous arguments suggested particle mobility drives symmetry breaking in 2D Vicsek models.

Purpose of the Study:

  • To investigate symmetry breaking in 2D classical hard-core particle models with Vicsek-type exchange interactions.
  • To determine if these models exhibit spontaneous rotational symmetry breaking at nonzero temperatures.
  • To provide a counterexample to existing theories on symmetry breaking origins.

Main Methods:

  • Extension of the Hohenberg-Mermin-Wagner theorem for absence of spontaneous magnetization.
  • Application of the McBryan-Spencer bound for correlation functions.
  • Mathematical proof for equilibrium states at nonzero temperatures.

Main Results:

  • The studied models do not spontaneously break rotational symmetry in their equilibrium states.
  • This holds true for any nonzero temperature.
  • The findings challenge the established link between particle mobility and symmetry breaking.

Conclusions:

  • The origin of symmetry breaking in these models is not particle mobility.
  • Absence of detailed balance or nonequilibrium conditions are suggested as the true origins.
  • Provides a new perspective on symmetry breaking in dynamic systems.