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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.17483 |
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Table of Contents:
- We study the thermodynamic geometry of the one-dimensional Blume--Capel model within the Tsallis nonextensive framework to understand how generalized statistics modify correlation structure and pseudo-critical behaviour. Using the transfer matrix method, we construct the Tsallis entropy based thermodynamic metric as its negative Hessian on the parameter space $(β, J)$, with the crystal-field anisotropy $D$ as a control parameter, and compute the associated scalar curvature $R(T)$ as a measure of correlations. Although no true phase transition occurs in one dimension, $R(T)$ exhibits finite peaks signaling pseudo-critical crossovers. We analyze both $D < J$ and $D > J$ regimes and show that deviations from the Boltzmann--Gibbs limit ($q=1$) systematically deform the curvature profile: for $q>1$ the peak shifts and correlations persist beyond the crossover, whereas for $q<1$ the peak is weakened or suppressed. Our results demonstrate that the Tsallis parameter $q$ geometrically reshapes the entropy surface, providing a clear information-geometric interpretation of nonextensive effects in spin-1 systems.