Comment on: Discontinuous codimension-two bifurcation in a Vlasov equation (arXiv:2212.01250)
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| Format: | Preprint |
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2026
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| _version_ | 1866910066066587648 |
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| author | Teles, Tarcísio N. Pakter, Renato Levin, Yan |
| author_facet | Teles, Tarcísio N. Pakter, Renato Levin, Yan |
| contents | We comment on the recent work by Yamaguchi and Barré [Phys. Rev. E 107, 054203 (2023)], which uses linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian Mean Field (gHMF) model. By performing extensive molecular dynamics simulations with $N=10^8$ particles, we demonstrate that the bifurcation analysis of the initial stationary distribution is insufficient to predict either the location or the nature of the phase transition to a quasi-stationary state (qSS). Specifically, we show that for bimodal momentum distributions, the instability threshold identified by the authors does not correspond to a ferromagnetic transition; instead, the system remains in a paramagnetic state characterized by magnetization oscillations with a zero time-average. We find that the true paramagnetic-ferromagnetic transition is discontinuous (first-order) and occurs at significantly larger coupling strengths, characterized by a clear coexistence of states. These results indicate that linear bifurcation and symmetry-breaking phase transitions are distinct phenomena in long-range interacting systems, and that the former lacks the predictive power to describe the long-time fate of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22066 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comment on: Discontinuous codimension-two bifurcation in a Vlasov equation (arXiv:2212.01250) Teles, Tarcísio N. Pakter, Renato Levin, Yan Statistical Mechanics We comment on the recent work by Yamaguchi and Barré [Phys. Rev. E 107, 054203 (2023)], which uses linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian Mean Field (gHMF) model. By performing extensive molecular dynamics simulations with $N=10^8$ particles, we demonstrate that the bifurcation analysis of the initial stationary distribution is insufficient to predict either the location or the nature of the phase transition to a quasi-stationary state (qSS). Specifically, we show that for bimodal momentum distributions, the instability threshold identified by the authors does not correspond to a ferromagnetic transition; instead, the system remains in a paramagnetic state characterized by magnetization oscillations with a zero time-average. We find that the true paramagnetic-ferromagnetic transition is discontinuous (first-order) and occurs at significantly larger coupling strengths, characterized by a clear coexistence of states. These results indicate that linear bifurcation and symmetry-breaking phase transitions are distinct phenomena in long-range interacting systems, and that the former lacks the predictive power to describe the long-time fate of the system. |
| title | Comment on: Discontinuous codimension-two bifurcation in a Vlasov equation (arXiv:2212.01250) |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2603.22066 |