dorsal/arxiv
View SchemaCriticality in a Vlasov-Poisson system - a fermionic universality class
| Authors | A. V. Ivanov, S. V. Vladimirov, P. A. Robinson |
|---|---|
| Categories | |
| ArXiv ID | physics/0409091 |
| URL | https://arxiv.org/abs/physics/0409091 |
| DOI | 10.1103/PhysRevE.71.056406 |
Abstract
A model Vlasov--Poisson system is simulated close the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power--law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality $d=5$ below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead it corresponds to the propagator for the fermionic {\it vector} field and to the {\it upper critical dimensionality} $d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as representative of the {\it universality class} of critical phenomena of {\it a fermionic} quantum field description.
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"abstract": "A model Vlasov--Poisson system is simulated close the point of marginal\nstability, thus assuming only the wave-particle resonant interactions are\nresponsible for saturation, and shown to obey the power--law scaling of a\nsecond-order phase transition. The set of critical exponents analogous to those\nof the Ising universality class is calculated and shown to obey the Widom and\nRushbrooke scaling and Josephson\u0027s hyperscaling relations at the formal\ndimensionality $d=5$ below the critical point at nonzero order parameter.\nHowever, the two-point correlation function does not correspond to the\npropagator of Euclidean quantum field theory, which is the Gaussian model for\nthe Ising universality class. Instead it corresponds to the propagator for the\nfermionic {\\it vector} field and to the {\\it upper critical dimensionality}\n$d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as\nrepresentative of the {\\it universality class} of critical phenomena of {\\it a\nfermionic} quantum field description.",
"arxiv_id": "physics/0409091",
"authors": [
"A. V. Ivanov",
"S. V. Vladimirov",
"P. A. Robinson"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1103/PhysRevE.71.056406",
"title": "Criticality in a Vlasov-Poisson system - a fermionic universality class",
"url": "https://arxiv.org/abs/physics/0409091"
},
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