Haldar Arijit, Tavakol Omid, Ma Han, Scaffidi Thomas
Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada.
S. N. Bose National Centre for Basic Sciences, JD Block, Sector-III, Salt Lake City, Kolkata-700 106, India.
Phys Rev Lett. 2023 Sep 29;131(13):131601. doi: 10.1103/PhysRevLett.131.131601.
The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and high-energy systems. In this work, we perform an exact microscopic study of such a complex CFT (CCFT) in the two-dimensional O(n) loop model. The well-known absence of symmetry-breaking of the O(n>2) model is understood as arising from the displacement of the nontrivial fixed points into the complex temperature plane. Thanks to a numerical finite-size study of the transfer matrix, we confirm the presence of a CCFT in the complex plane and extract the real and imaginary parts of the central charge and scaling dimensions. By comparing those with the analytic continuation of predictions from Coulomb gas techniques, we determine the range of validity of the analytic continuation to extend up to n_{g}≈12.34, beyond which the CCFT gives way to a gapped state. Finally, we propose a beta function which reproduces the main features of the phase diagram and which suggests an interpretation of the CCFT as a liquid-gas critical point at the end of a first-order transition line.
最近有人提出，在调谐参数的复平面中隐藏着附近的共形场论（CFT），这为凝聚态物质和高能系统中普遍存在的“弱一级”相变提供了一个优雅的解释。在这项工作中，我们对二维O(n)环模型中的这种复共形场论（CCFT）进行了精确的微观研究。众所周知，O(n>2)模型不存在对称性破缺，这被理解为非平凡不动点向复温度平面的位移所致。通过对转移矩阵的数值有限尺寸研究，我们证实了复平面中存在CCFT，并提取了中心荷和标度维数的实部和虚部。通过将这些结果与库仑气体技术预测的解析延拓进行比较，我们确定了解析延拓的有效范围可扩展到ng≈12.34，超过这个值，CCFT会让位于一个有能隙的状态。最后，我们提出了一个β函数，它再现了相图的主要特征，并暗示将CCFT解释为一级相变线末端的液-气临界点。
