Researchers have conducted a Monte Carlo analysis of two-matrix models, specifically $ABBA$, $A\{B,A\}B$, and $ABAB$, to estimate the boundary of maximal convergence. The models, defined by hermitian matrices $A$ and $B$, involve a complex interplay of trace operations and parameters $g$ and $h$. By applying Monte Carlo methods, the study aims to pinpoint the critical curve that separates convergent and divergent regions in the parameter space. The investigation focuses on the behavior of these models under various conditions, including the impact of $g$ and $h$ on the convergence boundary1. This research has implications for understanding complex systems and phase transitions in statistical mechanics and quantum field theory. The findings of this study are crucial for practitioners working with matrix models, as they provide valuable insights into the convergence properties of these systems, ultimately informing the development of more accurate and efficient computational methods.
Critical curve of two-matrix models $ABBA$, $A\{B,A\}B$ and $ABAB$, Part I: Monte Carlo
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Why This Matters
Abstract: 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.
References
- [Author/Org]. (2026, March 26). Critical curve of two-matrix models $ABBA$, $A\{B,A\}B$ and $ABAB$, Part I: Monte Carlo. *arXiv Quantum Physics*. https://arxiv.org/abs/2603.25715v1
Original Source
arXiv Quantum Physics
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