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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.05192 |
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Table of Contents:
- Accurate determination of higher-order pressure derivatives with respect to temperature $T$ and chemical potential $μ$ is essential for analyzing critical phenomena, transport properties, and phase transitions in strongly interacting matter. However, standard numerical differentiation methods often suffer from large numerical instabilities, especially in more complex mean-field thermal field theories. In this work, we present an approach that systematically derives symbolic expressions for these higher-order derivatives, bypassing the numerical instabilities commonly encountered in conventional methods. Our formalism is based on a Jacobian technique, which ensures that the dependence of internal mean-field parameters is fully incorporated into the final symbolic expressions. We illustrate the effectiveness of this method using the two-flavor Nambu-Jona-Lasinio model as an example and show that it is particularly advantageous near phase transitions and at low temperatures, where numerical differentiation becomes highly sensitive.