Critical curve of two-matrix models $ABBA$, $A\{B,A\}B$ and $ABAB$, Part I: Monte Carlo
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917363270549504 |
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| author | Sánchez, Carlos I. Pérez |
| author_facet | Sánchez, Carlos I. Pérez |
| contents | For a family of two-matrix models \[ \frac{1}{2} \operatorname{Tr}(A^2+B^2) - \frac{g}{4} \operatorname{Tr}(A^4+B^4) - \begin{cases} \frac{h}{2} \operatorname{Tr}( A BA B) \\ \frac{h}{4} \operatorname{Tr}( A BA B+ ABBA ) \\ \frac{h}{2} \operatorname{Tr}( A B BA )
\end{cases}
\] with hermitian $A$ and $B$, we provide, in each case, a Monte Carlo estimate of the boundary of the maximal convergence domain in the $(h,g)$-plane. The results are discussed comparing with exact solutions (in agreement with the only analytically solved case) and phase diagrams obtained by means of the functional renormalization group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical curve of two-matrix models $ABBA$, $A\{B,A\}B$ and $ABAB$, Part I: Monte Carlo Sánchez, Carlos I. Pérez Mathematical Physics High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics 60B20, 82M31, 81-08, 81-04 For a family of two-matrix models \[ \frac{1}{2} \operatorname{Tr}(A^2+B^2) - \frac{g}{4} \operatorname{Tr}(A^4+B^4) - \begin{cases} \frac{h}{2} \operatorname{Tr}( A BA B) \\ \frac{h}{4} \operatorname{Tr}( A BA B+ ABBA ) \\ \frac{h}{2} \operatorname{Tr}( A B BA ) \end{cases} \] with hermitian $A$ and $B$, we provide, in each case, a Monte Carlo estimate of the boundary of the maximal convergence domain in the $(h,g)$-plane. The results are discussed comparing with exact solutions (in agreement with the only analytically solved case) and phase diagrams obtained by means of the functional renormalization group. |
| title | Critical curve of two-matrix models $ABBA$, $A\{B,A\}B$ and $ABAB$, Part I: Monte Carlo |
| topic | Mathematical Physics High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics 60B20, 82M31, 81-08, 81-04 |
| url | https://arxiv.org/abs/2603.25715 |