Related papers: Partition function zeros of zeta-urns
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…
We report on a new method to extract thermodynamic properties from the density of partition function zeroes on finite lattices. This allows direct determination of the order and strength of phase transitions numerically. Furthermore, it…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
We present methods that provide all zeroes and extrema of a function that do not require differentiation. Using point process theory, we are able to describe the locations of zeroes or maxima, their number, as well as their distribution…
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.…
We study the collapse transition of the lattice homopolymer on a square lattice by calculating the exact partition function zeros. The exact partition function is obtained by enumerating the number of possible conformations for each energy…
The aim of the present paper is to study the relations between the prime distribution and the zero distribution for generalized zeta functions which are expressed by Euler products and is analytically continued as meromorphic functions of…
We study the zeros of the $q$-state Potts model partition function $Z(\Lambda,q,v)$ for large $q$, where $v$ is the temperature variable and $\Lambda$ is a section of a regular $d$-dimensional lattice with coordination number…
Partition function of beta-gamma systems on the orbifolds C^2/Z_N and C^3/Z_M x Z_N are obtained as the invariant part of that on the respective affine spaces, by lifting the geometric action of the orbifold group to the fields.…
In this paper, we consider the physical meaning of the zeros and poles of partition function. We consider three different systems, including the harmonic oscillator in one dimension, Riemann zeta function and the quasinormal modes of black…
Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the…
For a function field $k$ over a finite field with $\mathbb{F}_q$ as the field of constant, and a finite abelian group $G$ whose exponent is divisible by $q-1$, we study the distribution of zeta zeroes for a random $G$-extension of $k$,…
We study the zeros in the complex plane of the partition function for the Ising model coupled to $2d$ quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two…
The paper reviews existing results about the statistical distribution of zeros for the three main types of zeta functions: number-theoretical, geometrical, and dynamical. It provides necessary background and some details about the proofs of…
Lee-Yang and Fisher zeros are crucial for the study of phase transitions in the grand canonical and the canonical ensembles, respectively. However, these powerful methods do not cover the isothermal-isobaric ensemble (NPT ensemble), which…
For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with…
We study the limiting behavior of the zeros of the zeta series of a finite poset under iterated barycentric subdivision, and we indicate the possibility of its application to number theory.
The (partially) ordered set of the non-trivial zeros of the zeta function with positive imaginary parts is considered. The order is the coordinatewise order inherited from $\mathbb{C}$. Some interesting properties regarding the minimal…
The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…