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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.11153 |
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| _version_ | 1866916625015373824 |
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| author | Akin, Kutay Berker, A. Nihat |
| author_facet | Akin, Kutay Berker, A. Nihat |
| contents | The random-field XY model is studied in spatial dimensions d=3 and 4, and in-between, as the limit q --> \infty of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower-critical dimension is determined between 3.81 < d_c <4. When the random-field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random-field is scaled with q^2, a universal phase diagram is found at intermediate temperatures in d=3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11153 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line Akin, Kutay Berker, A. Nihat Statistical Mechanics Disordered Systems and Neural Networks The random-field XY model is studied in spatial dimensions d=3 and 4, and in-between, as the limit q --> \infty of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower-critical dimension is determined between 3.81 < d_c <4. When the random-field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random-field is scaled with q^2, a universal phase diagram is found at intermediate temperatures in d=3. |
| title | Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2203.11153 |