Dohm Volker, Wessel Stefan
Institute for Theoretical Physics, RWTH Aachen University, 52056 Aachen, Germany.
Phys Rev Lett. 2021 Feb 12;126(6):060601. doi: 10.1103/PhysRevLett.126.060601.
The exact critical Casimir amplitude is derived for anisotropic systems within the d=2 Ising universality class by combining conformal field theory with anisotropic φ^{4} theory. Explicit results are presented for the general anisotropic scalar φ^{4} model and for the fully anisotropic triangular-lattice Ising model in finite rectangular and infinite strip geometries with periodic boundary conditions. These results demonstrate the validity of multiparameter universality for confined anisotropic systems and the nonuniversality of the critical Casimir amplitude. We find an unexpected complex form of self-similarity of the anisotropy effects near the instability where weak anisotropy breaks down. This can be traced back to the property of modular invariance of isotropic conformal field theory for d=2. More generally, for d>2 we predict the existence of self-similar structures of the finite-size scaling functions of O(n)-symmetric systems with planar anisotropies and periodic boundary conditions both in the critical region for n≥1 as well as in the Goldstone-dominated low-temperature region for n≥2.
通过将共形场论与各向异性φ⁴理论相结合，推导出了d = 2伊辛普适类中各向异性系统的精确临界卡西米尔振幅。给出了一般各向异性标量φ⁴模型以及具有周期性边界条件的有限矩形和无限条带几何结构中的完全各向异性三角晶格伊辛模型的明确结果。这些结果证明了受限各向异性系统多参数普适性的有效性以及临界卡西米尔振幅的非普适性。我们在不稳定性附近发现了各向异性效应的一种意想不到的自相似复形式，其中弱各向异性会失效。这可以追溯到d = 2的各向同性共形场论的模不变性性质。更一般地，对于d>2，我们预测在n≥1的临界区域以及n≥2的戈德斯通主导的低温区域中，具有平面各向异性和周期性边界条件的O(n)对称系统的有限尺寸标度函数存在自相似结构。
