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Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class

by Maciej Łebek, Paweł Jakubczyk

Submission summary

As Contributors: Pawel Jakubczyk · Maciej Łebek
Arxiv Link: (pdf)
Date accepted: 2021-05-28
Date submitted: 2021-02-09 13:05
Submitted by: Łebek, Maciej
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Statistical and Soft Matter Physics
Approach: Theoretical


We analyze the thermodynamic Casimir effect in strongly anizotropic systems from the vectorial $N\to\infty$ class in a slab geometry. Employing the imperfect (mean-field) Bose gas as a representative example, we demonstrate the key role of spatial dimensionality $d$ in determining the character of the effective fluctuation-mediated interaction between the confining walls. For a particular, physically conceivable choice of anisotropic dispersion and periodic boundary conditions, we show that the Casimir force at criticality as well as within the low-temperature phase is repulsive for dimensionality $d\in (\frac{5}{2},4)\cup (6,8)\cup (10,12)\cup\dots$ and attractive for $d\in (4,6)\cup (8,10)\cup \dots$. We argue, that for $d\in\{4,6,8\dots\}$ the Casimir interaction entirely vanishes in the scaling limit. We discuss implications of our results for systems characterized by $1/N>0$ and possible realizations in the context of quantum phase transitions.

Published as SciPost Phys. Core 4, 016 (2021)

List of changes

1. We substantially broadened the non-technical introductory part (Section I).
2. We improved the presentation of the most important aspects of the studied model (Section II).
3. We elaborated on the physical context of anisotropic systems in our work (Section I&II).
4. We added a discussion of the large N limit in the context of our system (Section IV).
5. We extended the list of references.

Reports on this Submission

Anonymous Report 2 on 2021-4-1 (Invited Report)


The authors have satisfactorily replied to the points raised by myself and the other referee and the paper is now suitable for publication.

  • validity: -
  • significance: -
  • originality: -
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Anonymous Report 1 on 2021-3-1 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2009.10718v2, delivered 2021-03-01, doi: 10.21468/SciPost.Report.2636


I have gone through the Authors' letter (in response to the
reviews), the previous Referee reports and the amended manuscrit. In
my view the Authors have diligently addressed mosy of the issues raised
earlier, have incorporated new references and corrected the draft to
all round satisfaction.

In the light of this, my recommendation is: The new version can be
accepted for publication

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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