Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition
We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution [L. Onsager, Phys. Rev. 65, 117 (1944)0031-899X10.1103/PhysRev.65.117; B. Kaufman, Phys. Rev...
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-02-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.013086 |
| _version_ | 1797210579037847552 |
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| author | Zhiyuan Wang Kaden R. A. Hazzard |
| author_facet | Zhiyuan Wang Kaden R. A. Hazzard |
| author_sort | Zhiyuan Wang |
| collection | DOAJ |
| description | We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution [L. Onsager, Phys. Rev. 65, 117 (1944)0031-899X10.1103/PhysRev.65.117; B. Kaufman, Phys. Rev. 76, 1232 (1949)0031-899X10.1103/PhysRev.76.1232] of the 2D Ising model and the solution of Kitaev's honeycomb model [A. Kitaev, Ann. Phys, 321, 2 (2006)0003-491610.1016/j.aop.2005.10.005], leading to a three-parameter phase diagram with a third-order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions. |
| first_indexed | 2024-04-24T10:12:50Z |
| format | Article |
| id | doaj.art-62545250962847aea4f99e953608d749 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:50Z |
| publishDate | 2023-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-62545250962847aea4f99e953608d7492024-04-12T17:28:14ZengAmerican Physical SocietyPhysical Review Research2643-15642023-02-015101308610.1103/PhysRevResearch.5.013086Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transitionZhiyuan WangKaden R. A. HazzardWe study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution [L. Onsager, Phys. Rev. 65, 117 (1944)0031-899X10.1103/PhysRev.65.117; B. Kaufman, Phys. Rev. 76, 1232 (1949)0031-899X10.1103/PhysRev.76.1232] of the 2D Ising model and the solution of Kitaev's honeycomb model [A. Kitaev, Ann. Phys, 321, 2 (2006)0003-491610.1016/j.aop.2005.10.005], leading to a three-parameter phase diagram with a third-order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions.http://doi.org/10.1103/PhysRevResearch.5.013086 |
| spellingShingle | Zhiyuan Wang Kaden R. A. Hazzard Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition Physical Review Research |
| title | Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition |
| title_full | Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition |
| title_fullStr | Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition |
| title_full_unstemmed | Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition |
| title_short | Topological correlations in three-dimensional classical Ising models: An exact solution with a continuous phase transition |
| title_sort | topological correlations in three dimensional classical ising models an exact solution with a continuous phase transition |
| url | http://doi.org/10.1103/PhysRevResearch.5.013086 |
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