Random transverse and longitudinal field Ising chains
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908958407524352 |
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| author | Petö, Tamás Iglói, Ferenc Kovács, István A. |
| author_facet | Petö, Tamás Iglói, Ferenc Kovács, István A. |
| contents | Motivated by experimental results on compounds like ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider an Ising chain with random bonds in the simultaneous presence of random transverse and longitudinal fields. We study the low-energy properties of the model at zero temperature by the strong disorder renormalization group (SDRG) method.In the absence of random longitudinal fields, the model showcases a trivial quantum-ordered and quantum-disordered fixed-point and a non-trivial infinite disorder critical point. In the absence of random transverse fields, the behavior is dictated by the classical random-field Ising fixed-point. In the simultaneous presence of both a longitudinal and transverse random field, the RG trajectories are attracted to one of the two disordered fixed-points and the relevant scaling direction at the infinite disorder fixed-point is along the separatrix, where the correlation-length is shown to diverge with an exponent $ν_h \approx 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random transverse and longitudinal field Ising chains Petö, Tamás Iglói, Ferenc Kovács, István A. Disordered Systems and Neural Networks Motivated by experimental results on compounds like ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider an Ising chain with random bonds in the simultaneous presence of random transverse and longitudinal fields. We study the low-energy properties of the model at zero temperature by the strong disorder renormalization group (SDRG) method.In the absence of random longitudinal fields, the model showcases a trivial quantum-ordered and quantum-disordered fixed-point and a non-trivial infinite disorder critical point. In the absence of random transverse fields, the behavior is dictated by the classical random-field Ising fixed-point. In the simultaneous presence of both a longitudinal and transverse random field, the RG trajectories are attracted to one of the two disordered fixed-points and the relevant scaling direction at the infinite disorder fixed-point is along the separatrix, where the correlation-length is shown to diverge with an exponent $ν_h \approx 1$. |
| title | Random transverse and longitudinal field Ising chains |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2501.02643 |