# Partition function zeros for aperiodic systems

@article{Baake1995PartitionFZ, title={Partition function zeros for aperiodic systems}, author={Michael Baake and Uwe Grimm and Carmelo Pisani}, journal={Journal of Statistical Physics}, year={1995}, volume={78}, pages={285-297} }

The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices. Here, we consider magnetic field and temperature zeros of Ising model partition functions on several aperiodic structures. In 1D, we analyze aperiodic chains obtained from substitution rules, the most prominent example being the Fibonacci chain. In 2D, we…

## 19 Citations

Lee-Yang zeros for substitutional systems

- Physics, Mathematics
- 1995

Qualitative and quantitative information about critical phenomena is provided by the distribution of zeros of the partition function in the complex plane. We apply this idea to Ising models on…

ZEROS FOR SUBSTITUTIONAL SYSTEMS

- 2008

Qualitative and quantitative information about critical phenomena is provided by the distribution of zeros of the partition function in the complex plane. We apply this idea to Ising models on…

Lee - Yang zeros in the scaling region of a two-dimensional quasiperiodic Ising model

- Mathematics
- 1997

Quasiperiodic, planar Ising models with ferromagnetic nearest-neighbour interactions should show the same universal critical behaviour as the classical Ising model on the square lattice. We use the…

Partition function zeros of the antiferromagnetic spin-12 Ising–Heisenberg model on a diamond chain

- Mathematics
- 2014

A critical Ising model on the Labyrinth

- Physics, Mathematics
- 1994

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a…

Uniform Hyperbolicity for Szeg\H{o} Cocycles and Applications to Random CMV Matrices and the Ising Model

- Mathematics, Physics
- 2014

We consider products of the matrices associated with the Szeg\H{o} recursion from the theory of orthogonal polynomials on the unit circle and show that under suitable assumptions, their norms grow…

Orthogonal Polynomials on the Unit Circle with Fibonacci Verblunsky Coefficients, II. Applications

- Mathematics, Physics
- 2013

We consider CMV matrices with Verblunsky coefficients determined in an appropriate way by the Fibonacci sequence and present two applications of the spectral theory of such matrices to problems in…

Lee-Yang zeros of periodic and quasiperiodic anisotropic XY chains in a transverse field.

- Physics, MedicinePhysical review letters
- 2006

It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field.

Partition function zeros of the one-dimensional Potts model: the recursive method

- Mathematics, Physics
- 2002

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.…

Properties of 1D Classical and Quantum Ising Models: Rigorous Results

- Mathematics
- 2014

In this paper, we consider one-dimensional classical and quantum spin-1/2 quasi-periodic Ising chains, with two-valued nearest neighbor interaction modulated by a Fibonacci substitution sequence on…

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