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| Formato: | Preprint |
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2024
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| Acceso en línea: | https://arxiv.org/abs/2410.19069 |
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| author | Vedula, Bharadwaj Moore, M. A. Sharma, Auditya |
| author_facet | Vedula, Bharadwaj Moore, M. A. Sharma, Auditya |
| contents | We have studied the diluted Heisenberg spin glass model in a 3-component random field for the commonly-used one-dimensional long-range model where the probability that two spins separated by a distance $r$ interact with one another falls as $1/r^{2 σ}$, for two values of $σ$, $0.75$ and $0.85$. No de Almeida-Thouless line is expected at these $σ$ values. The spin glass correlation length $ξ_{\text{SG}}$ varies with the random field as expected from the Imry-Ma argument and the droplet scaling picture of spin glasses. However, when $ξ_{\text{SG}}$ becomes comparable to the system size $L$, there are departures which we attribute to the features deriving from the TNT picture of spin glasses. For the case $σ=0.85$ these features go away for system sizes with $L >L^*$, where $L^*$ is large ($\approx 4000-8000$ lattice spacings). In the case of $σ= 0.75$ we have been unable to study large enough systems to determine its value of $L^*$. We sketch a renormalization group scenario to explain how these features could arise. On this scenario finite size effects on the droplet scaling picture in low-dimensional spin glasses produce TNT features and some aspects of Parisi's replica symmetry breaking theory of the Sherrington-Kirkpatrick model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nature of spin glass order in physical dimensions Vedula, Bharadwaj Moore, M. A. Sharma, Auditya Disordered Systems and Neural Networks We have studied the diluted Heisenberg spin glass model in a 3-component random field for the commonly-used one-dimensional long-range model where the probability that two spins separated by a distance $r$ interact with one another falls as $1/r^{2 σ}$, for two values of $σ$, $0.75$ and $0.85$. No de Almeida-Thouless line is expected at these $σ$ values. The spin glass correlation length $ξ_{\text{SG}}$ varies with the random field as expected from the Imry-Ma argument and the droplet scaling picture of spin glasses. However, when $ξ_{\text{SG}}$ becomes comparable to the system size $L$, there are departures which we attribute to the features deriving from the TNT picture of spin glasses. For the case $σ=0.85$ these features go away for system sizes with $L >L^*$, where $L^*$ is large ($\approx 4000-8000$ lattice spacings). In the case of $σ= 0.75$ we have been unable to study large enough systems to determine its value of $L^*$. We sketch a renormalization group scenario to explain how these features could arise. On this scenario finite size effects on the droplet scaling picture in low-dimensional spin glasses produce TNT features and some aspects of Parisi's replica symmetry breaking theory of the Sherrington-Kirkpatrick model. |
| title | Nature of spin glass order in physical dimensions |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2410.19069 |