Two-time correlation functions of a system of Bose particles are studied. We find relation of zeros of the correlation functions with the Lee-Yang zeros of partition function of the system. Obtained relation gives the possibility to observe the Lee-Yang zeros experimentally. A particular case of Bose particles on two levels is examined and zeros of two-time correlation functions and Lee-Yang zeros of partition function of the system are analyzed.
Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We find that the distribution of zeros of partition functions for these models in one dimension (1d) can be obtained analytically. We prove that all the LY zeros are real and negative for such models with arbitrary blockade radii. Therefore, no phase trans…
Yang-Lee zeros of the one-dimensional Q-state Potts model
研究了任意Q和温度下一维铁磁和反铁磁Q态Potts模型的Yang-Lee零点的分布。首次全面研究了Potts反铁磁体的Yang-Lee零点。Yang-Lee零点的分布呈现出各种不同的形状。有些杨-李零点甚至在T>0时也位于正实轴上。对于铁磁模型，这只发生在Q<1的情况下，而反铁磁模型在正实轴上存在一些零点，对于Q <1 and for Q>1。
Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices
研究了递归格上Q-态Potts模型的Yang-Lee零点。将一维晶格看作配位数为2的Bethe晶格，利用中性周期点的概念，全面分析了一维铁磁和反铁磁Potts模型的Yang-Lee零点的位置.当Q>1和0<Q1时，发现了三种不同的Yang-Lee零点区域<1. An exact analytical formula for the equation of phase transition points is derived for the 1D case. It is shown that Yang-Lee zeros of the Q-state Potts model on a Bethe lattice are located on arcs of circles with the radius depending on Q and temperature for Q>.研究了Q>1和0<Q<1情况下的复磁场亚稳区。计算了一维和Bethe晶格Potts模型的Yang-Lee边缘奇异性指数。数值研究了不同Q值时亚稳区的动力学行为。
A general analytical formula for recurrence relations of multisite interaction Ising models in an external magnetic field on the Cayley-type lattices is derived. Using the theory of complex analytical dynamics on the Riemann sphere, a numerical algorithm to obtain Yang-Lee and Fisher zeros of the models is developed. It is shown that the sets of Yang-Lee and Fisher zeros are almost always fractals, that could be associated with Mandelbrot-like sets on the complex magnetic field and temperature planes respectively.
We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are able to determine the convergence point of the Lee-Yang zeros in the thermodynamic limit and thereby predict the occurrence of a phase transition. The cumulant method is attractive from an experimental point of view since it uses fluctuations of measurable quantities, such as the magnetization in a spin lattice, and it can be applied to a variety of equilibri…
The Yang-Lee edge singularity is a quintessential nonunitary critical phenomenon accompanied by anomalous scaling laws. However, an imaginary magnetic field involved in this critical phenomenon makes its physical implementation difficult. By invoking the quantum-classical correspondence to embed the Yang-Lee edge singularity in a quantum system with an ancilla qubit, we demonstrate a physical realization of the nonunitary quantum criticality in an open quantum system. Here the nonunitary criticality is identified with the singularity at an exceptional point caused by postselection of quantum m…
Phase Transition is associated with a drastic change in some observable (ordered parameter) of the system when the controlled parameter is tuned smoothly. Lee-Yang theory of phase transition is discussed which is related to the accumulation of singularities of free energy, equivalently complex roots of Grand Partition function (Partition function) at points on positive real axis in complex fugacity plane; and more general (p+1) phase system is discussed, and also the case when (w+2) phases coexist together. Comparison to Mayer's theory is also presented.
Comment on "First-order phase transitions: equivalence between bimodalities and the Yang-Lee theorem"
本文讨论了Chomaz和Gulminelli [Physica A 330（2003）451]最近提出的关于一阶相变的两种定义的等价性的一个结果的有效性。我表明，零的配分函数满足杨-李定理的条件的分布不一定与非凹微正则熵函数，或等价地，与正则分布的平均能量具有双峰形状，所声称的Chomaz和Gulminelli。事实上，这样的零点分布也可以与凹熵函数和具有仿射部分的单峰正则分布相关联。一个简单的例子详细说明了这一微妙之处。
We determine the universal location of the Yang-Lee edge singularity in the entire relevant domain of spatial dimensions $1\le d \le 4$ for the Ising universality class. To that end, we present analytical results for $d=1,2,4$ and near four dimensions. For $d=3$ and a set of fractional dimensions, we perform numerical calculations using a systematic Functional Renormalization Group approach.
We describe classical stochastic processes by using dynamical Lee-Yang zeros. The system is in contact with external leads and the time evolution is described by the two-state classical master equation. The cumulant generating function is written in a factorized form and the current distribution of the system is characterized by the dynamical Lee-Yang zeros. We show that a continuous distribution of zeros is obtained by discretizing the time variable. When the transition probability is a periodically-oscillating function of time, the distribution of zeros splits into many parts. We study the g…
Phase transitions are typically accompanied by non-analytic behaviors of the free energy, which can be explained by considering the zeros of the partition function in the complex plane of the control parameter and their approach to the critical value on the real-axis as the system size is increased. Recent experiments have shown that partition function zeros are not just a theoretical concept. They can also be determined experimentally by measuring fluctuations of thermodynamic observables in systems of finite size. Motivated by this progress, we investigate here the partition function zeros f…
