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Size effects in finite systems with long-range interactions.

E S Loscar1, C M Horowitz2

  • 1Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP, CCT La Plata-CONICET, Calle 59 no. 789, B1900BTE La Plata, Argentina and Departamento de Física, Universidad Nacional de La Plata, c.c. 67, 1900 La Plata, Argentina.

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This summary is machine-generated.

We generalized the Tsallis conjecture for systems with broken symmetry, enabling better study of finite-size effects in systems with long-range interactions. This approach adjusts interaction strength for systems with broken translational invariance.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Small systems with long-range interactions show significant size effects.
  • The Tsallis conjecture describes scaling in translationally invariant systems.

Purpose of the Study:

  • To generalize the Tsallis conjecture to systems with broken translational symmetry.
  • To provide a method for studying finite-size effects in such systems.

Main Methods:

  • Adjusting a parameter to define an effective distance for interaction strength.
  • Applying the generalized conjecture to a 1D Ising model with power-law decaying ferromagnetic interactions (1/r^{1+σ}).

Main Results:

  • The generalized conjecture effectively studies finite-size effects in systems with broken symmetry.
  • Demonstrated the approach on the 1D Ising model.

Conclusions:

  • The proposed generalization of the Tsallis conjecture is a convenient tool for analyzing finite-size effects.
  • This method offers an alternative to traditional finite-size scaling theory for specific systems.