Panero, Marco (2007) Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere. JOURNAL OF HIGH ENERGY PHYSICS (5): 082. ISSN 1029-8479
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We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the role they play in the "striped phase", pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. Next, we test a quantitative, non-trivial theoretical prediction for this model, which has been formulated in the literature: The existence of an eigenvalue sector characterised by a precise probability density, and the emergence of the phase transition associated with the opening of a gap around the origin in the eigenvalue distribution. The theoretical predictions are confirmed by our numerical results. Finally, we propose a possible method to detect numerically the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUANTUM-FIELD THEORY; MONTE-CARLO CALCULATIONS; LATTICE GAUGE-THEORIES; NON-COMMUTATIVITY; PHASE-STRUCTURE; HEAT-BATH; GEOMETRY; SPACES; GRAVITY; RENORMALIZATION; non-commutative geometry; nonperturbative effects; matrix models |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Petra Gürster |
| Date Deposited: | 29 Oct 2020 09:44 |
| Last Modified: | 29 Oct 2020 09:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/32832 |
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