Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929565497032704 |
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| author | Aguilar-Janita, Miguel Martin-Mayor, Victor Moreno-Gordo, Javier Ruiz-Lorenzo, Juan Jesus |
| author_facet | Aguilar-Janita, Miguel Martin-Mayor, Victor Moreno-Gordo, Javier Ruiz-Lorenzo, Juan Jesus |
| contents | The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical -- but not generally accepted -- field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00569 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field Aguilar-Janita, Miguel Martin-Mayor, Victor Moreno-Gordo, Javier Ruiz-Lorenzo, Juan Jesus Disordered Systems and Neural Networks The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical -- but not generally accepted -- field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation. |
| title | Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2306.00569 |