Dynamical phase transitions in the nonreciprocal Ising model
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915218162974720 |
|---|---|
| author | Avni, Yael Fruchart, Michel Martin, David Seara, Daniel Vitelli, Vincenzo |
| author_facet | Avni, Yael Fruchart, Michel Martin, David Seara, Daniel Vitelli, Vincenzo |
| contents | Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the phase transition from static to time-dependent states are not yet fully understood. To address these questions, we study a minimalistic system endowed with nonreciprocal interactions: an Ising model with two spin species having opposing goals. The mean-field equation predicts three stable phases: disorder, static order, and a time-dependent swap phase. Large scale numerical simulations support the following: (i) in 2D, the swap phase is destabilized by defects; (ii) in 3D, the swap phase is stable, and has the properties of a time crystal; (iii) the transition from disorder to swap in 3D is characterized by the critical exponents of the 3D XY model, and corresponds to the breaking of a continuous symmetry, time translation invariance; (iv) when the two species have fully anti-symmetric couplings, the static-order phase is unstable in any finite dimension due to droplet growth; (v) in the general case of asymmetric couplings, static order can be restored by a droplet-capture mechanism preventing the droplets from growing indefinitely. We provide details on the full phase diagram which includes first- and second-order-like phase transitions and study how the system coarsens into swap and static-order states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07481 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical phase transitions in the nonreciprocal Ising model Avni, Yael Fruchart, Michel Martin, David Seara, Daniel Vitelli, Vincenzo Statistical Mechanics Soft Condensed Matter Pattern Formation and Solitons Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the phase transition from static to time-dependent states are not yet fully understood. To address these questions, we study a minimalistic system endowed with nonreciprocal interactions: an Ising model with two spin species having opposing goals. The mean-field equation predicts three stable phases: disorder, static order, and a time-dependent swap phase. Large scale numerical simulations support the following: (i) in 2D, the swap phase is destabilized by defects; (ii) in 3D, the swap phase is stable, and has the properties of a time crystal; (iii) the transition from disorder to swap in 3D is characterized by the critical exponents of the 3D XY model, and corresponds to the breaking of a continuous symmetry, time translation invariance; (iv) when the two species have fully anti-symmetric couplings, the static-order phase is unstable in any finite dimension due to droplet growth; (v) in the general case of asymmetric couplings, static order can be restored by a droplet-capture mechanism preventing the droplets from growing indefinitely. We provide details on the full phase diagram which includes first- and second-order-like phase transitions and study how the system coarsens into swap and static-order states. |
| title | Dynamical phase transitions in the nonreciprocal Ising model |
| topic | Statistical Mechanics Soft Condensed Matter Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2409.07481 |