Introduction to Monte Carlo for matrix models
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large N limit. The results we obtain agree with exact analytic expres- sions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved m...
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| Format: | Article |
| Language: | English |
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SciPost
2022-04-01
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| Series: | SciPost Physics Lecture Notes |
| Online Access: | https://scipost.org/SciPostPhysLectNotes.46 |
| _version_ | 1818773954294185984 |
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| author | Raghav G. Jha |
| author_facet | Raghav G. Jha |
| author_sort | Raghav G. Jha |
| collection | DOAJ |
| description | We consider a wide range of matrix models and study them using the Monte Carlo technique in the large N limit. The results we obtain agree with exact analytic expres- sions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, N, and the required precision. |
| first_indexed | 2024-12-18T10:33:27Z |
| format | Article |
| id | doaj.art-5d022285fb2b44908c0b11cc5c47921e |
| institution | Directory Open Access Journal |
| issn | 2590-1990 |
| language | English |
| last_indexed | 2024-12-18T10:33:27Z |
| publishDate | 2022-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Lecture Notes |
| spelling | doaj.art-5d022285fb2b44908c0b11cc5c47921e2022-12-21T21:10:48ZengSciPostSciPost Physics Lecture Notes2590-19902022-04-014610.21468/SciPostPhysLectNotes.46Introduction to Monte Carlo for matrix modelsRaghav G. JhaWe consider a wide range of matrix models and study them using the Monte Carlo technique in the large N limit. The results we obtain agree with exact analytic expres- sions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, N, and the required precision.https://scipost.org/SciPostPhysLectNotes.46 |
| spellingShingle | Raghav G. Jha Introduction to Monte Carlo for matrix models SciPost Physics Lecture Notes |
| title | Introduction to Monte Carlo for matrix models |
| title_full | Introduction to Monte Carlo for matrix models |
| title_fullStr | Introduction to Monte Carlo for matrix models |
| title_full_unstemmed | Introduction to Monte Carlo for matrix models |
| title_short | Introduction to Monte Carlo for matrix models |
| title_sort | introduction to monte carlo for matrix models |
| url | https://scipost.org/SciPostPhysLectNotes.46 |
| work_keys_str_mv | AT raghavgjha introductiontomontecarloformatrixmodels |