Ising model on generalized Union Jack lattice
Source abstract
Abstract
The Ising model is generalized to two translations on Union Jack lattice with interactions between the spins at the nearest and noncrossing diagonal neighbor sites. Exact analytical expressions are derived for the largest eigenvalue of the Kramers-Wannier transfer matrix as well as for the spontaneous magnetization, taking into account the specified interactions (six parameters of exchange interactions on the whole). The thermodynamic and frustration properties of the model are investigated. The essential features of the behavior of entropy, heat capacity and spontaneous magnetization are revealed. A number of exact expressions for phase-transition temperatures, zero-temperature entropy (residual entropy) and zero-temperature spontaneous magnetization (residual spontaneous magnetization) are obtained. Especially replete with new effects, the model under consideration manifests itself in a wide variety of special cases and relationships with other lattices, including new lattices found and not previously investigated.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Theoretical and Computational Physics · Opinion Dynamics and Social Influence · Complex Systems and Time Series Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (36)
Show source-provided references
1. Crystal statistics. I. A two-dimensional model with an order-disorder transition10.1103/PhysRev.65.117 ↗
2. A combinatorial solution of the two-dimensional ising model10.1103/PhysRev.88.1332 ↗
3. The combinatrial method and the two-dimensional ising model10.1143/PTP.13.38 ↗
4. New solution of the ising problem for a rectangular lattice10.1063/1.1731333 ↗
5. A calculation of the partition function for a plane dipole lattice
6. Spontaneous magnetization of a plane dipole lattice
7. Feynman · 1972 · 136
8. Order-disorder in hexagonal lattices10.1016/0031-8914(50)90130-3 ↗
9. Antiferromagnetism. The triangular ising net10.1103/PhysRev.79.357 ↗
10. Antiferromagnetism. The kagomé ising net10.1143/ptp/10.2.158 ↗
11. Spontaneous magnetization, a generalized square lattice10.1143/PTP.23.374 ↗
12. Exact spontaneous magnetisation of an ising model on the 3-12 lattice10.1088/0022-3719/19/27/022 ↗
13. Spontaneous magnetisation of the ising model on a 3-12 lattice10.1088/0305-4470/20/16/041 ↗
14. Comments on the spontaneous magnetization of the ising model on a 4–8 lattice10.1016/0375-9601(87)90495-6 ↗
15. Spontaneous magnetization, a generalized square lattice
16. Two-dimensional ising model on a ruby lattice10.1088/0305-4470/16/16/027 ↗
17. Two-dimensional ising model on a 4-6-12 lattice10.1071/PH850227 ↗
18. Ising model with interaction between nonnearest neighbors
19. A simple example of exactly solvable models with reentrant phenomena10.1143/PTP.78.1242 ↗
20. Spontaneous magnetization of the ising model on a union Jack lattice10.1016/0375-9601(87)90507-X ↗
21. Reentrant transition of the ising model on the centred square lattice10.1088/0305-4470/19/9/040 ↗
22. Note on the ising model with second-neighbour and four-body interactions pertaining to universality10.1143/PTP.62.1225 ↗
23. Note on the ising model with second-neighbour and four-body interactions pertaining to universality10.1143/PTP.40.462 ↗
24. Reentrant transition of the ising model on the centred square lattice10.1088/0305-4470/20/16/049 ↗
25. Spontaneous magnetization of the ising model
26. Spontaneous magnetization of the ising model on a square lattice with non-crossing diagonal interactions10.1016/0375-9601(87)90874-7 ↗
27. Spontaneous magnetization of the ising model on the union Jack lattice10.1016/0375-9601(87)90162-9 ↗
28. Statistics of the two-dimensional ferromagnet. Part II10.1103/PhysRev.60.263 ↗
29. Theory of the frustration effect in spin glasses: I
30. Theory of the frustration effect: II. Ising spins on a square lattice10.1088/0022-3719/10/18/008 ↗
31. General lattice model of phase transitions10.1103/PhysRevB.2.723 ↗
32. 32-Vertex model on the triangular lattice10.1088/0305-4470/8/11/013 ↗
33. Correction to metamagnetic conditions of the union Jack lattice ising model10.1142/S0129183118500638 ↗
34. General lattice model of phase transitions10.1103/PhysRevB.42.10570 ↗
35. The spin-1/2 ising model on the bow-tie lattice as an exactly soluble free-Fermion model10.12693/APhysPolA.113.457 ↗
36. Exact curie temperature for the ising model on archimedean and laves lattices10.1088/1751-8113/43/38/385002 ↗