Faculty of Physics, University of Athens, GR-15784 Athens, Greece.
Phys Rev E. 2017 May;95(5-1):052145. doi: 10.1103/PhysRevE.95.052145. Epub 2017 May 30.
We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of the isothermal critical exponent δ. In the thermodynamic limit the zeros belonging to this class condense to the critical point ζ=1 on the real axis in the complex fugacity plane while the complementary set of zeros (with Reζ<1) covers the unit circle. Although the aforementioned class degenerates to a single point for an infinite system, when the size is finite it contributes significantly to the partition function and reflects the self-similar structure (fractal geometry, scaling laws) of the critical system. This property opens up the perspective to formulate finite-size scaling theory in effective QCD, near the chiral critical point, in terms of the location of Lee-Yang zeros.
我们表明，在临界温度下，一般标量场论的配分函数存在一类李-杨零点，其位置与系统大小成比例，特征指数用等温和临界指数 δ 表示。在热力学极限下，属于这个类的零点在复化学势平面上的实轴上凝聚到临界点 ζ=1，而互补的零点集（Reζ<1）覆盖单位圆。尽管对于无限大系统，上述类退化到一个单点，但当系统大小有限时，它对配分函数有显著贡献，并反映了临界系统的自相似结构（分形几何、标度律）。这一特性为在有效 QCD 中，在手征临界点附近，根据李-杨零点的位置来制定有限尺寸标度理论提供了可能性。
