Physics Research Institute, Southern Federal University, 194 Stachki Avenue, Rostov-on-Don, 344090 Russia.
Department of Physics, Laurentian University, Sudbury, Ontario, Canada P3E 2C6 and Department of Physics, McGill University, Montréal, Quebec, Canada H3A 2T8.
Phys Rev E. 2017 Dec;96(6-1):062123. doi: 10.1103/PhysRevE.96.062123. Epub 2017 Dec 15.
We report exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions (also known as disorder lines or geometric phase transitions). The phase transition is signaled by a change of asymptotic behavior of the nonlocal string-string correlation functions when their monotonic decay becomes modulated by incommensurate oscillations. The transitions occur for rarefied (m-periodic) strings with arbitrary odd m. We propose a duality transformation which maps the Ising chain onto the m-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs. Then the m-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the m-leg tube. We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in m-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.
磁场中的经典反铁磁伊辛链。我们表明，该模型具有无限级联的热相变（也称为无序线或几何相变）。相变由非局部字符串-字符串相关函数的渐近行为的变化来指示，当它们的单调衰减被非齐次振荡调制时。对于具有任意奇数 m 的稀薄（m 周期）字符串，会发生这种转变。我们提出了一种对偶变换，将伊辛链映射到具有沿腿的最近邻耦合和相邻腿的 plaquette 四自旋相互作用的 m 腿伊辛管。然后，伊辛链的 m 字符串相关函数被映射到 m 腿管腿上的两点自旋-自旋相关函数。我们将这些相变级联的起源追溯到伊辛链在 m 周期复磁场中的李-杨零点线，从而使我们能够将这些零点与可观察到的（并且可能可测量的）量联系起来。
