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Introduction to Monte Carlo for Matrix Models
by Raghav G. Jha
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Raghav Govind Jha 
Submission information  

Preprint Link:  scipost_202111_00064v2 (pdf) 
Code repository:  https://github.com/rgjha/MMMC 
Date accepted:  20220325 
Date submitted:  20220318 19:32 
Submitted by:  Jha, Raghav Govind 
Submitted to:  SciPost Physics Lecture Notes 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
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 multimatrix 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.
Author comments upon resubmission
List of changes
1. We have merged Sec.3.1 with Sec.2 and renamed the section.
2. We have added 12 paragraphs regarding the MetropolisHastings algorithm as the simplest example of MCMC (Markov chain Monte Carlo).
3. For the bosonic fields, it is certainly possible to use heatbath, but the article introduces HMC since it is more natural when advancing to field theories with fermions where usually RHMC is used (rational HMC). We have made a comment about this in the article.
4. We have introduced “BoxMuller algorithm” in Sec.3.2.1.
5. We have corrected the fact that Ref. [39] did not study D0 model and added the four references.
6. We have added future directions as suggested by the first referee and added references.
Published as SciPost Phys. Lect. Notes 46 (2022)
Anonymous on 20220318 [id 2301]
We thank both the referees for their comments and address them below, starting with the second referee report.
I hope these changes make the version2 of the article (attached) ready to be published. Thank you.