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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2501.05192 |
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| _version_ | 1866916558979203072 |
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| author | Gholami, Hosein |
| author_facet | Gholami, Hosein |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Calculation of Pressure Derivatives in Mean-Field Thermal Field Theories Gholami, Hosein High Energy Physics - Phenomenology Nuclear Theory Computational Physics 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. |
| title | On the Calculation of Pressure Derivatives in Mean-Field Thermal Field Theories |
| topic | High Energy Physics - Phenomenology Nuclear Theory Computational Physics |
| url | https://arxiv.org/abs/2501.05192 |