Hyperuniformity in Ashkin-Teller model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909583615721472 |
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| author | Mukherjee, Indranil Mohanty, P. K. |
| author_facet | Mukherjee, Indranil Mohanty, P. K. |
| contents | We show that equilibrium systems in $d$ dimension that obey the inequality $dν> 2,$ known as Harris criterion, exhibit suppressed energy fluctuation in their critical state. Ashkin-Teller model is an example in $d=2$ where the correlation length exponent $ν$ varies continuously with the inter-spin interaction strength $λ$ and exceeds the value $\frac d2$ set by Harris criterion when $λ$ is negative; there, the variance of the subsystem energy across a length scale $l$ varies as $l^{d-α}$ with hyperuniformity exponent $α= 2(1-ν^{-1}).$ Point configurations constructed by assigning unity to the sites which has coarse-grained energy beyond a threshold value also exhibit suppressed number fluctuation and hyperuniformiyty with same exponent $α.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperuniformity in Ashkin-Teller model Mukherjee, Indranil Mohanty, P. K. Statistical Mechanics We show that equilibrium systems in $d$ dimension that obey the inequality $dν> 2,$ known as Harris criterion, exhibit suppressed energy fluctuation in their critical state. Ashkin-Teller model is an example in $d=2$ where the correlation length exponent $ν$ varies continuously with the inter-spin interaction strength $λ$ and exceeds the value $\frac d2$ set by Harris criterion when $λ$ is negative; there, the variance of the subsystem energy across a length scale $l$ varies as $l^{d-α}$ with hyperuniformity exponent $α= 2(1-ν^{-1}).$ Point configurations constructed by assigning unity to the sites which has coarse-grained energy beyond a threshold value also exhibit suppressed number fluctuation and hyperuniformiyty with same exponent $α.$ |
| title | Hyperuniformity in Ashkin-Teller model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.20266 |