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

TL;DR

This paper investigates how spatial dimensionality influences the sign and magnitude of thermodynamic Casimir forces in strongly anisotropic systems within the large N limit, revealing dimension-dependent attraction, repulsion, or null interactions.

Contribution

It demonstrates the critical role of dimensionality in determining the nature of Casimir forces in anisotropic systems using the imperfect Bose gas as a model.

Findings

Casimir force is repulsive for certain dimensions and attractive for others.

At specific dimensions, the Casimir interaction vanishes in the scaling limit.

Results have implications for quantum phase transitions and systems with finite N.

Abstract

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.