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Linked-Cluster Expansion of the Ising Model

Massimo Campostrini B

arXiv:cond-mat/0005130Journal of Statistical PhysicsApr 1, 200115 citations

Cluster expansion and path-integral methods for the transverse Ising model

Zhen‐Ya Li, Qing Jiang

Physics Letters AJul 1, 198921 citations

Adaptive cluster expansion for Ising spin models

Simona Cocco, Giancarlo Croce, Francesco Zamponi

arXiv:1906.05805The European Physical Journal BNov 1, 20192 citations

Longitudinal magnetic field effect on thermodynamic properties of the XXZ-model with easy-axis type magnetic anisotropy. The two-particle cluster approximation

Р. Р. Левицкий, O. R. Baran

ВПЛИВ ПОЗДОВЖНЬОГО МАГНЕТНОГО ПОЛЯ НА ТЕРМОДИНАМIЧНI ВЛАСТИВОСТI XXZ-МОДЕЛI З МАГНЕТНОЮ АНIЗОТРОПIЄЮ ТИПУ ЛЕГКА ВIСЬ.НАБЛИЖЕННЯ ДВОЧАСТИНКОВОГО КЛАСТЕРА Р. Р. Левицький, О

Journal of Physical StudiesJan 1, 20040 citations

Spin- Ising model by the cluster variation method and the path probability method

Osman Canko, Mustafa Keskín

Physica A Statistical Mechanics and its ApplicationsSep 7, 200514 citations

Yang-Lee zeros of two-dimensional nearest-neighbor antiferromagnetic Ising models: A numerical linked cluster expansion study

Mahmoud Abdelshafy, Muhammad Sedik

We study Yang-Lee zeros as they approach the thermodynamic limit of the two-dimensional (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 $T\ensuremath{\ll}{T}_{c}$, the results suggest that two vertical lines at $\ifmmode\pm\else\textpm\fi{}{h}_{c}(T)$ in the complex field plane (i.e., two concentric circles in the complex fugacity plane) are the thermodynamic root curves. A similar picture is found 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.We study Yang-Lee zeros as they approach the thermodynamic limit of the two-dimensional (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 $T\ensuremath{\ll}{T}_{c}$, the results suggest that two vertical lines at $\ifmmode\pm\else\textpm\fi{}{h}_{c}(T)$ in the complex field plane (i.e., two concentric circles in the complex fugacity plane) are the thermodynamic root curves. A similar picture is found 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.

arXiv:2503.14602Physical review. B./Physical review. BAug 8, 20252 citations

Thermodynamics of Ising model within cluster expansion method

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Thermodynamics of Ising model within cluster expansion method

Abstract

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