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Two-dimensional Ising model with the next nearest interactions
1Chinese Academy of Sciences, Institute of Metal Research, Shenyang National Laboratory for Materials Science, 72 Wenhua Road, Shenyang 110016, People's Republic of China.
Physical Review. E
|July 24, 2026
Summary
This study analytically derives the partition function and spontaneous magnetization for a 2D Ising model with next-nearest interactions. Findings show increased interactions and topological contributions enhance the critical point in Ising lattices.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Materials Science
Background:
- The two-dimensional (2D) Ising model is a fundamental framework for studying magnetism.
- Understanding the influence of interactions beyond nearest neighbors is crucial for accurate magnetic material modeling.
Purpose of the Study:
- To analytically derive the partition function and spontaneous magnetization for a 2D Ising model with next-nearest interactions at zero magnetic field.
- To investigate the role of topological structures and interaction complexity on the critical point of Ising lattices.
Main Methods:
- Analysis of transfer matrices in Clifford algebraic, transfer tensor, and schematic representations.
- Modification of 3D Ising model approaches for the 2D system with extended interactions.
- Comparison of derived solutions with exact solutions for other Ising lattices.
Main Results:
- The partition function and spontaneous magnetization were analytically obtained for the specified 2D Ising model.
- The system's equivalence to a modified triangular Ising model was established.
- A correlation between increased interactions/topological contributions and an enhanced critical point was identified.
Conclusions:
- The analytical solution provides insights into the behavior of 2D magnetic systems with complex interactions.
- Increased interaction complexity and topological features significantly influence the critical temperature of Ising lattices.
- The findings aid in understanding the physical properties of 2D magnetic materials.
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