相关论文: Exact Zeros of the Partition Function for a Contin…
We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…
We discuss the distribution of partition function zeros for the grand-canonical ensemble of the zeta-urn model, where tuning a single parameter can give a first or any higher order condensation transition. We compute the locus of zeros for…
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 zeros of complex Gaussian random polynomials, with coefficients such that the density in the underlying complex space is uniform, are known to have the same statistical properties as the zeros of the coherent state representation of…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
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…
This paper explores the use of a cumulant method to determine the zeros of partition functions for continuous phase transitions. Unlike a first-order transition, with a uniform density of zeros near the transition point, a continuous…
The zeros of the size-$n$ partition functions for a statistical mechanical model can be used to help understand the critical behaviour of the model as $n\to\infty$. Here we use weighted Dyck paths as a simple model of two-dimensional…
We discuss a numerical analysis employing the density of partition function zeroes which permits effective distinction between phase transitions of first and second order, elucidates crossover between such phase transitions and gives a new…
We characterize the breaking of analyticity with respect to the replica number which occurs in random energy models via the complex zeros of the moment of the partition function. We perturbatively evaluate the zeros in the vicinity of the…
In this paper we study finite-size effects in the Blume-Capel model through the analysis of the zeros of the partition function. We consider a complete graph and make use of the behaviour of the partition function zeros to elucidate the…
Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d. complex Gaussian coefficients a_n. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the…
The equation of state of a system at equilibrium may be derived from the canonical or the grand canonical partition function. The former is a function of temperature T, while the latter also depends on the chemical potential \mu for…
Phase transitions are one of the most interesting natural phenomena. For finite systems, one of the concerns in the topic is how to classify a specific transition as being of first, second, or even of a higher order, according to the…
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…
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 real temperature, and for complex temperature and real magnetic field, respectively. We…
The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems. An exact recurrence relation for the partition function is derived. It is shown that zeros of the partition…
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that…
We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann-Cartan or…