Configurational Temperature in Matrix Models and Random Matrix Ensembles

Anosh Joseph; Vinod Mamale

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arXiv · 2606.28148

Configurational Temperature in Matrix Models and Random Matrix Ensembles

Anosh Joseph·Vinod Mamale

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Abstract

We investigate the configurational temperature estimator in interacting matrix models and Gaussian random-matrix ensembles. The estimator follows from an exact Schwinger--Dyson identity and may be expressed in terms of the gradient and Hessian of the action. We study the Gross--Witten--Wadia model, a quartic double-well matrix model, and the Gaussian Orthogonal, Unitary, and Symplectic Ensembles. In all cases, the estimator satisfies the exact Schwinger--Dyson identity, $\beta_{\rm config} = 1$, within statistical uncertainties. Separating the estimator into isotropic and anisotropic parts, we find that the leading finite-$N$ corrections satisfy the approximate relation $\beta_{\rm iso} - 1 \simeq - \beta_{\rm aniso}$. We also show that the configurational temperature estimator provides a sensitive diagnostic of Monte Carlo simulations.

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Anosh Joseph, Vinod Mamale. 2026-06-26. Configurational Temperature in Matrix Models and Random Matrix Ensembles. https://arxiv.org/abs/2606.28148

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