Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
arXiv:2503.14602 · doi:10.1103/x38c-w4z2
Abstract
We study Yang-Lee zeros in the thermodynamic limit of the 2D nearest-neighbor antiferromagnetic Ising model on square and triangular lattices. We employ the Numerical Linked Cluster Expansion (NLCE) equipped with Exact Enumeration (EE) of the partition function to estimate the Laplacian of the free energy, which is proportional to the zeros density. Using a modified NLCE, where the expansion can be carried directly on the Yang-Lee zeros of the involved clusters, we estimate the density of Yang-Lee zeros in the thermodynamic limit. NLCE gives significantly more zeros than EE in the complex field plane providing more insights on how the root curves look in the thermodynamic limit. For the square lattice at , the results suggest that two vertical lines at in the complex field plane (i.e two concentric circles in the complex fugacity plane) are the thermodynamic root curves. A similar picture is expected for the triangular lattice for phase transitions at large values of magnetic field while further study is needed for phase transitions at smaller values of magnetic field. The convergence of the NLCE and (EE) calculations of the partition function to the thermodynamic limit is studied in both lattices and the temperature-field phase diagram is obtained from Yang-Lee zeros using both methods. This NLCE-based approach will facilitate the study of different types of phase transitions using Yang-Lee zeros in future research.
References in corpus (28)
- Observation of Lee-Yang zeros
- Numerical Linked-Cluster Approach to Quantum Lattice Models
- Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
- A Short Introduction to Numerical Linked-Cluster Expansions
- Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
- Experimental Determination of Dynamical Lee-Yang Zeros
- General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions
- Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
- Possible inversion symmetry breaking in the pyrochlore Heisenberg magnet
- Linked cluster expansions for open quantum systems on a lattice
- Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
- Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model
- Optimization of finite-size errors in finite-temperature calculations of unordered phases
- Yang-Lee Zeros, Semicircle Theorem, and Nonunitary Criticality in Bardeen-Cooper-Schrieffer Superconductivity
- Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
- Experimental observation of the Yang-Lee quantum criticality in open systems
- Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
- Numerical linked cluster expansions for inhomogeneous systems
- Yang-Lee Zeros of the Triangular Ising Antiferromagnets
- Linked-cluster expansion for the Green's function of the infinite-U Hubbard model
- Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective
- Yang-Lee Zeros of the Yang-Lee Model
- Lee-Yang theory of the superradiant phase transition in the open Dicke model
- Lee-Yang Zeros of the antiferromagnetic Ising Model
- Lee-Yang zeros in the Rydberg atoms
- L-based numerical linked cluster expansion for square lattice models
- Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions
- Yang-Lee Zeros of Certain Antiferromagnetic Models