Related papers: Characterization of Lee-Yang polynomials

Results of somewhat mysterious nature are known on the location of zeros of certain polynomials associated with statistical mechanics (Lee-Yang circle theorem) and also with graph counting. In an attempt at clarifying the situation we…

A Lee-Yang polynomial $ p(z_{1},\ldots,z_{n}) $ is a polynomial that has no zeros in the polydisc $ \mathbb{D}^{n} $ and its inverse $ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n} $. We show that any real-rooted exponential polynomial of…

Lee-Yang theory, based on the study of zeros of the partition function, is widely regarded as a powerful and complimentary approach to the study of critical phenomena and forms a foundational part of the theory of phase transitions. Its…

Let $Z_n(z,t)$ denote the partition function of the $q$-state Potts Model on the rooted binary Cayley tree of depth~$n$. Here, $z = {\rm e}^{-h/T}$ and $t = {\rm e}^{-J/T}$ with $h$ denoting an externally applied magnetic field, $T$ the…

We present a generalized circle theorem which includes the Lee-Yang theorem for symmetric transitions as a special case. It is found that zeros of the partition function can be written in terms of discontinuities in the derivatives of the…

Let $z_1, \dots, z_m$ be $m$ distinct complex numbers, normalized to $|z_k| = 1$, and consider the polynomial $$ p_{m}(z) = \prod_{k=1}^{m}{(z-z_k)}.$$ We define a sequence of polynomials in a greedy fashion, $$ p_{N+1}(z) = p_{N}(z)…

A complex tensor with $n$ binary indices can be identified with a multilinear polynomial in $n$ complex variables. We say it is a Lee-Yang tensor with radius $r$ if the polynomial is nonzero whenever all variables lie in the open disk of…

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by…

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…

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We derive formulas for the positions and the density of the zeros. In particular, we show that…

The hot nucleus $^{162}\mathrm{Dy}$ is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee-Yang's theorem is applied to classify the pairing phase transition by…

Lee-Yang zeros are points on the complex plane of magnetic field where the partition function of a spin system is zero and therefore the free energy diverges. Lee-Yang zeros and their generalizations are ubiquitous in many-body systems and…

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…

We consider polynomials on the unit circle defined by the recurrence relation \Phi_{k+1}(z) = z \Phi_{k} (z) - \bar{\alpha}_{k} \Phi_k^{*}(z) for k \geq 0 and \Phi_0=1. For each n we take \alpha_0, \alpha_1, ...,\alpha_{n-2} i.i.d. random…

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems.…

Let $P(z)$ be a polynomial of degree $n$ having no zero in $|z|<k$ where $k\geq 1,$ then for every real or complex number $\alpha$ with $|\alpha|\geq 1$ it is known \begin{equation*} \underset{|z|=1}{\max}|D_\alpha P(z)|\leq…

Let $p(z)=a_0+a_1z+a_2z^2+a_3z^3+\cdots+a_nz^n$ be a polynomial of degree $n,$ where the coefficients $a_j,$ $j \in \{0,1,2,\cdots n\},$ may be complex. We impose some restriction on the coefficients of the real part of the given polynomial…

We evaluate the number of monic polynomials (of arbitrary degree $N$) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the following, we call polynomials with this property {\em…

We apply the Yang-Lee theory of phase transitions to an urn model of separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity $z$. Numerical…

Lee, in a series of papers, described a unified formulation of the statistical thermodynamics of ideal quantum gases in terms of the polylogarithm functions, $\textup{Li}_{s} (z)$. It is aimed here to investigate the functions…