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Scaling behavior for finite O(n) systems with long-range interaction.

H Chamati1, N S Tonchev

  • 1Institute of Solid State Physics, 72 Tzarigradsko Chaussée, 1784 Sofia, Bulgaria. chamati@issp.bas.bg

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

This study explores scaling properties in O(n) systems with long-range interactions. Thermodynamic functions depend on a scaling variable involving coupling constants and system size, yielding universal results.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Understanding scaling properties is crucial for characterizing phase transitions in physical systems.
  • Long-range interactions significantly influence the behavior of many-body systems.

Purpose of the Study:

  • To investigate the scaling properties of fully finite O(n) systems with algebraic long-range interactions.
  • To compute scaling functions and analyze thermodynamic dependencies below the upper critical dimension.

Main Methods:

  • Utilizing a one-loop order computation for scaling functions in the nonzero modes.
  • Employing an expansion in powers of sqrt[epsilon], where epsilon = 2sigma - d, up to O(epsilon(3/2)).

Main Results:

  • Derived expressions for thermodynamic functions dependent on a scaling variable z = RU^(-1/2)L^(2-eta-epsilon/2).

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  • Identified R and U as coupling constants within the effective theory.
  • Obtained simple universal results for the system's behavior.

    • Conclusions:

    • The scaling behavior of these systems is governed by a universal scaling variable.
    • The findings provide insights into the critical phenomena of systems with specific interaction types.