Eigenvalue-flipping algorithm for matrix Monte Carlo

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Authors

KOVÁČIK Samuel TEKEL Juraj

Year of publication 2022
Type Article in Periodical
Magazine / Source Journal of High Energy Physics
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007/JHEP04(2022)149
Doi http://dx.doi.org/10.1007/JHEP04(2022)149
Keywords Algorithms and Theoretical Developments; Matrix Models; Non-Commutative Geometry; Lattice Quantum Field Theory
Description Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method, which is efficient for small matrix sizes but cannot guarantee ergodicity when working with large ones. In this paper, we propose an improvement of the algorithm that, for a large class of matrix models, allows to tunnel between various vacua in a proficient way, where sign change of eigenvalues is proposed externally. We test the method on two models: the pure potential matrix model and the scalar field theory on the fuzzy sphere.
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