Critical exponents of the spin glass transition in a field at zero temperature
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917361230020608 |
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| author | Angelini, Maria Chiara Palazzi, Saverio Parisi, Giorgio Rizzo, Tommaso |
| author_facet | Angelini, Maria Chiara Palazzi, Saverio Parisi, Giorgio Rizzo, Tommaso |
| contents | We analyze the spin glass transition in a field in finite dimension $D$ below the upper critical dimension directly at zero temperature using a recently introduced perturbative loop expansion around the Bethe lattice solution. The expansion is generated by the so-called $M$-layer construction, and it has $1/M$ as the associated small parameter. Computing analytically and numerically these non-standard diagrams at first order in the $1/M$ expansion, we construct an $ε$-expansion around the upper critical dimension $D_\text{uc}=8$, with $ε=D_\text{uc}-D$. Following standard field theoretical methods, we can write a $β$ function, finding a new zero-temperature fixed-point associated with the spin glass transition in a field in dimensions $D<8$. We are also able to compute, at first order in the $ε$-expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical exponents of the spin glass transition in a field at zero temperature Angelini, Maria Chiara Palazzi, Saverio Parisi, Giorgio Rizzo, Tommaso Disordered Systems and Neural Networks We analyze the spin glass transition in a field in finite dimension $D$ below the upper critical dimension directly at zero temperature using a recently introduced perturbative loop expansion around the Bethe lattice solution. The expansion is generated by the so-called $M$-layer construction, and it has $1/M$ as the associated small parameter. Computing analytically and numerically these non-standard diagrams at first order in the $1/M$ expansion, we construct an $ε$-expansion around the upper critical dimension $D_\text{uc}=8$, with $ε=D_\text{uc}-D$. Following standard field theoretical methods, we can write a $β$ function, finding a new zero-temperature fixed-point associated with the spin glass transition in a field in dimensions $D<8$. We are also able to compute, at first order in the $ε$-expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent. |
| title | Critical exponents of the spin glass transition in a field at zero temperature |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2502.21089 |