Spin cones in random-field XY models
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929295294726144 |
|---|---|
| author | Pereira, Rajiv G Janardhanan, Ananya Barma, Mustansir |
| author_facet | Pereira, Rajiv G Janardhanan, Ananya Barma, Mustansir |
| contents | We determine the arrangement of spins in the ground state of the XY model with quenched, random fields, on a fully connected graph. Two types of disordered fields are considered, namely randomly oriented magnetic fields, and randomly oriented crystal fields. Orientations are chosen from a uniformly isotropic distribution, but disorder fluctuations in each realization of a finite system lead to a breaking of rotational symmetry. The result is an interesting pattern of spin orientations, found by solving a system of coupled, nonlinear equations within perturbation theory and also by exact numerical continuation. All spins lie within a cone for small enough ratio of field to coupling strength, with an interesting distribution of spin orientations, with peaks at the cone edges. The orientation of the cone depends strongly on the realization of disorder, but the opening angle does not. In the case of random magnetic fields, the cone angle widens as the ratio increases till a critical value at which there is a first order phase transition and the cone disappears. With random crystal fields, there is no phase transition and the cone angle approaches $180^\circ$ for large values of the ratio. At finite low temperatures, Monte-Carlo simulations show that the formation of a cone and its subsequent alignment along the equilibrium direction occur on two different time scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spin cones in random-field XY models Pereira, Rajiv G Janardhanan, Ananya Barma, Mustansir Statistical Mechanics Disordered Systems and Neural Networks We determine the arrangement of spins in the ground state of the XY model with quenched, random fields, on a fully connected graph. Two types of disordered fields are considered, namely randomly oriented magnetic fields, and randomly oriented crystal fields. Orientations are chosen from a uniformly isotropic distribution, but disorder fluctuations in each realization of a finite system lead to a breaking of rotational symmetry. The result is an interesting pattern of spin orientations, found by solving a system of coupled, nonlinear equations within perturbation theory and also by exact numerical continuation. All spins lie within a cone for small enough ratio of field to coupling strength, with an interesting distribution of spin orientations, with peaks at the cone edges. The orientation of the cone depends strongly on the realization of disorder, but the opening angle does not. In the case of random magnetic fields, the cone angle widens as the ratio increases till a critical value at which there is a first order phase transition and the cone disappears. With random crystal fields, there is no phase transition and the cone angle approaches $180^\circ$ for large values of the ratio. At finite low temperatures, Monte-Carlo simulations show that the formation of a cone and its subsequent alignment along the equilibrium direction occur on two different time scales. |
| title | Spin cones in random-field XY models |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2403.19939 |