Domain Growth in Long-range Ising Models with Disorder
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915493227528192 |
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| author | Agrawal, Ramgopal Corberi, Federico Lippiello, Eugenio Puri, Sanjay |
| author_facet | Agrawal, Ramgopal Corberi, Federico Lippiello, Eugenio Puri, Sanjay |
| contents | Recent advances have highlighted the rich low-temperature kinetics of the long-range Ising model (LRIM). This study investigates domain growth in an LRIM with quenched disorder, following a deep low-temperature quench. Specifically, we consider an Ising model with interactions that decay as $J(r) \sim r^{-(D+σ)}$, where $D$ is the spatial dimension and $σ> 0$ is the power-law exponent. The quenched disorder is introduced via random pinning fields at each lattice site. For nearest-neighbor models, we expect that domain growth during activated dynamics is logarithmic in nature: $R(t) \sim (\ln t)^α$, with growth exponent $α>0$. Here, we examine how long-range interactions influence domain growth with disorder in dimensions $D = 1$ and $D = 2$. In $D = 1$, logarithmic growth is found to persist for various $σ> 0$. However, in $D = 2$, the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Domain Growth in Long-range Ising Models with Disorder Agrawal, Ramgopal Corberi, Federico Lippiello, Eugenio Puri, Sanjay Statistical Mechanics Soft Condensed Matter Recent advances have highlighted the rich low-temperature kinetics of the long-range Ising model (LRIM). This study investigates domain growth in an LRIM with quenched disorder, following a deep low-temperature quench. Specifically, we consider an Ising model with interactions that decay as $J(r) \sim r^{-(D+σ)}$, where $D$ is the spatial dimension and $σ> 0$ is the power-law exponent. The quenched disorder is introduced via random pinning fields at each lattice site. For nearest-neighbor models, we expect that domain growth during activated dynamics is logarithmic in nature: $R(t) \sim (\ln t)^α$, with growth exponent $α>0$. Here, we examine how long-range interactions influence domain growth with disorder in dimensions $D = 1$ and $D = 2$. In $D = 1$, logarithmic growth is found to persist for various $σ> 0$. However, in $D = 2$, the dynamics is more complex due to the non-trivial interplay between extended interactions, disorder, and thermal fluctuations. |
| title | Domain Growth in Long-range Ising Models with Disorder |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2507.03154 |