Artun E Can, Berker A Nihat
TÜBITAK Research Institute for Fundamental Sciences, Gebze, Kocaeli 41470, Turkey.
Faculty of Engineering and Natural Sciences, Kadir Has University, Cibali, Istanbul 34083, Turkey.
Phys Rev E. 2023 Aug;108(2-1):024116. doi: 10.1103/PhysRevE.108.024116.
A spin system is studied with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalization-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: Conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first- and second-order phase transitions, themselves delimited by multicritical points: Inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.
研究了一个自旋系统，该系统在二维和三维空间中同时具有置换对称的Potts相互作用和自旋旋转对称的时钟相互作用。利用最近改进的（自发一阶检测）Migdal-Kadanoff近似的重整化群解，或者等效地，通过包含有效空位的分层晶格，计算了全局相图。发现了五种不同的有序相：传统有序铁磁相、四极相、反铁磁相以及代数有序反铁磁相、反四极相。这五种不同的有序相和无序相由一阶和二阶相变相互界定，而这些相变本身又由多临界点界定：反转双临界点、零温双临界点、三临界点、二阶分岔点和零温高度简并多临界点。一个丰富的相图拓扑结构展示了所有这些现象。
