PhysicsarXiv
Ranked by formulaVerdict: NotableQuantum Ising transition on the Cayley tree: boundary criticality, universality, and an effective Bethe line
We investigate quantum criticality in the transverse-field Ising model on finite Cayley trees and demonstrate that their extensive boundary fundamentally changes the nature of the quantum phase transition compared with…
Caveats
- Preprint; not yet peer reviewed.
VerdictWorth a reader's time today.
Abstract
We investigate quantum criticality in the transverse-field Ising model on finite Cayley trees and demonstrate that their extensive boundary fundamentally changes the nature of the quantum phase transition compared with the infinite, boundary-free Bethe lattice. Using tree tensor-network simulations for systems with up to N=12286 sites, we identify a boundary-driven continuous transition at h_x^c≈1.76, distinct from the mean-field Bethe-lattice transition at h_x^c≈2.23. We characterize this transition through finite-size scaling of the magnetization and magnetic susceptibility and extract a consistent set of critical exponents. By introducing next-nearest-neighbor interactions, we demonstrate the robustness of the extracted critical exponents, providing numerical argument for the Ising boundary universality class on the Cayley tree. Furthermore, we show that the physics of the boundary-free Bethe lattice can be efficiently recovered on a finite Cayley tree by fine-tuning a local boundary field. The resulting effective Bethe line, whose existence is tied to the mean-field nature of the bulk transition, effectively screens the extensive boundary and restores both the critical point and the mean-field critical scaling of the infinite Bethe lattice.
The editor's rubric
| Dimension | Level | Weight | What that level means |
|---|---|---|---|
| Leverage | ███░░ 3 | 18% | A method or resource many groups across the field will adopt within a year. |
| Magnitude | ██░░░ 2 | 20% | Solid incremental gain on a meaningful problem. |
| Evidence | ████░ 4 | 22% | Strong: large scale, preregistered, independently replicated, or a well-powered randomized trial. |
| Novelty | ███░░ 3 | 22% | A genuinely new approach to an open problem. |
| Trajectory | ███░░ 3 | 10% | A clear path to scale. |
| Stakes | ██░░░ 2 | 8% | Benefits a professional community (practitioners, clinicians, engineers). |
Editor’s rationale
Heuristic triage from title and abstract text only, not a reading of the paper. Cues found: method (we report); novelty (discovery); design (multicenter); scale (scalable, efficient).
How the score was computed
- Merit
- 5.9 / 10
- Adjusted merit
- 4.8 / 10
- Attention
- 0%
- Freshness
- 84%