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Casimir force in O(n) systems with a diffuse interface.

Daniel Dantchev1, Daniel Grüneberg

  • 1Fachbereich Physik, Universität Duisburg-Essen, Campus Duisburg, D-47048 Duisburg, Germany and Institute of Mechanics-BAS, Academic G. Bonchev St. bl. 4, 1113 Sofia, Bulgaria.

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Summary
This summary is machine-generated.

We investigated the Casimir force in anisotropic O(n) systems, finding it differs from isotropic systems even at critical temperatures. Diffuse interfaces lead to a repulsive Casimir force across all temperatures.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • The Casimir effect describes a physical force acting between two uncharged conductive bodies in a vacuum.
  • Anisotropic systems exhibit direction-dependent properties, potentially altering standard physical phenomena.
  • Diffuse interfaces represent a gradual transition between different material phases, impacting surface interactions.

Purpose of the Study:

  • To analyze the Casimir force in anisotropic O(n) systems with diffuse interfaces.
  • To compare the behavior of anisotropic systems with their isotropic counterparts.
  • To derive exact analytical results for scaling functions and critical behavior.

Main Methods:

  • Utilizing the O(n) model in d-dimensions (2
  • Applying antiperiodic boundary conditions along the finite dimension L.
  • Deriving exact analytical results for the n-->infinity limit.

Main Results:

  • The Casimir force, free energy, and helicity modulus differ in anisotropic systems compared to isotropic ones, even at the bulk critical temperature.
  • A relationship was established between the Casimir amplitudes of anisotropic and isotropic systems.
  • Exact analytical results for scaling functions and critical amplitudes were derived for d=3, revealing a repulsive Casimir force due to diffuse interfaces.

Conclusions:

  • Anisotropy and diffuse interfaces significantly modify the Casimir force, leading to repulsive interactions.
  • The derived scaling functions provide a comprehensive understanding of the system's behavior.
  • The findings are crucial for understanding interfacial phenomena in various physical systems.