Related papers: Partition function zeros of quantum many-body syst…
We prove that for the Ising model on a lattice of dimensionality $d \ge 2$, the zeros of the partition function $Z$ in the complex $\mu$ plane (where $\mu=e^{-2\beta H}$) lie on the unit circle $|\mu|=1$ for a wider range of $K_{n n'}=\beta…
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…
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…
To understand the distribution of the Yang-Lee zeros in quantum integrable field theories we analyse the simplest of these systems given by the two-dimensional Yang-Lee model. The grand-canonical partition function of this quantum field…
The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity $e^{h\Delta\tau}$, and the Euclidean-time lattice spacing $\Delta\tau$ can…
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…
The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the…
Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations have confirmed that the free energy of QCD is a quartic function of quark chemical potential at…
We study the partition function of the model formulated with Wilson fermions with only one species, both analytically and numerically. At strong coupling we construct the solution for lattice size up to $8\times 8$, a polynomial in the…
The $Q$-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on…
To simulate indistinguishable particles, recent studies of path-integral molecular dynamics formulated their partition function $Z$ as a recurrence relation involving a variable $\xi$, with $\xi=1$(-1) for bosons (fermions). Inspired by…
We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice, and the more tractable mean-field model corresponding to…
We study the Yang-Lee zeros of a random matrix partition function with the global symmetries of the QCD partition function. We consider both zeros in the complex chemical potential plane and in the complex mass plane. In both cases we find…
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…
We obtain in a closed form the 1/N^2 contribution to the free energy of the two Hermitian N\times N random matrix model with non symmetric quartic potential. From this result, we calculate numerically the Yang-Lee zeros of the 2D Ising…
Based on the chiral symmetry breaking pattern and the corresponding low-energy effective lagrangian, we determine the fermion mass dependence of the partition function and derive sum rules for eigenvalues of the QCD Dirac operator in finite…
We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding…
We report Lee-Yang zeros behavior at finite temperature and density. The quark number densities, <n>, are calculated at the pure imaginary chemical potential, where no sign problem occurs. Then, the canonical partition functions,…
Showing that the location of the zeros of the partition function can be used to study phase transitions, Yang and Lee initiated an ambitious and very fruitful approach. We give an overview of the results obtained using this approach. After…
In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a…