Probing the mesoscopics of competing interactions with the thermodynamic curvature: the case of a two-parameter ANNNI chain
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| Format: | Preprint |
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2024
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| _version_ | 1866909303264247808 |
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| author | Khatua, Soumen Sahay, Anurag |
| author_facet | Khatua, Soumen Sahay, Anurag |
| contents | This work examines the full scope of long-standing conjectures identifying the invariant thermodynamic curvature $R$ as the correlation volume $ξ^d$ and also as a measure of underlying statistical interactions. To this end, we set up a two-parameter ANNNI (Axial Next Nearest Neighbour Ising) chain featuring two next nearest neighbour (nnn) and a nearest neighbour (nn) interaction. Competition between interactions and resulting frustration engender a rich phase behaviour including a cross-over between two ferrimagnetic sub-phases. We show that $R$ attests to all its conjectured attributes with valuable insights into the character of mesoscopic fluctuating substructures. In a remarkable demonstration of its relevance at a far-from-critical point, $R$ is shown to resolve a hitherto unnoticed tricky issue involving $ξ$. A physically transparent expression for the zero field $R$ helps bring into focus the pivotal role played by some third order fluctuation moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probing the mesoscopics of competing interactions with the thermodynamic curvature: the case of a two-parameter ANNNI chain Khatua, Soumen Sahay, Anurag Statistical Mechanics Mesoscale and Nanoscale Physics This work examines the full scope of long-standing conjectures identifying the invariant thermodynamic curvature $R$ as the correlation volume $ξ^d$ and also as a measure of underlying statistical interactions. To this end, we set up a two-parameter ANNNI (Axial Next Nearest Neighbour Ising) chain featuring two next nearest neighbour (nnn) and a nearest neighbour (nn) interaction. Competition between interactions and resulting frustration engender a rich phase behaviour including a cross-over between two ferrimagnetic sub-phases. We show that $R$ attests to all its conjectured attributes with valuable insights into the character of mesoscopic fluctuating substructures. In a remarkable demonstration of its relevance at a far-from-critical point, $R$ is shown to resolve a hitherto unnoticed tricky issue involving $ξ$. A physically transparent expression for the zero field $R$ helps bring into focus the pivotal role played by some third order fluctuation moments. |
| title | Probing the mesoscopics of competing interactions with the thermodynamic curvature: the case of a two-parameter ANNNI chain |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2409.01643 |