Restoring isotropy in a three-dimensional lattice model: the Ising universality class
We study a generalized Blume-Capel model on the simple cubic lattice. In addition to the nearest-neighbor coupling there is a next-to-next-to-nearest-neighbor coupling. In order to quantify spatial anisotropy, we determine the correlation length in the high-temperature phase of the model for three d...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 July 2021
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| In: |
Physical review
Year: 2021, Volume: 104, Issue: 1, Pages: 1-17 |
| ISSN: | 2469-9969 |
| DOI: | 10.1103/PhysRevB.104.014426 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevB.104.014426 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevB.104.014426 
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| Author Notes: | Martin Hasenbusch |
MARC
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| 520 | |a We study a generalized Blume-Capel model on the simple cubic lattice. In addition to the nearest-neighbor coupling there is a next-to-next-to-nearest-neighbor coupling. In order to quantify spatial anisotropy, we determine the correlation length in the high-temperature phase of the model for three different spatial directions. It turns out that the spatial anisotropy depends very little on the dilution or crystal-field parameter D of the model and is essentially determined by the ratio of the nearest-neighbor and the next-to-next-to-nearest-neighbor coupling. This ratio is tuned such that the leading contribution to the spatial anisotropy is eliminated. Next we perform a finite-size scaling (FSS) study to tune D such that also the leading correction to scaling is eliminated. Based on this FSS study, we determine the critical exponents ν=0.62998(5) and η=0.036284(40), which are in nice agreement with the more accurate results obtained by using the conformal bootstrap method. Furthermore, we provide accurate results for fixed-point values of dimensionless quantities such as the Binder cumulant and for the critical couplings. These results provide the groundwork for broader studies of universal properties of the three-dimensional Ising universality class. | ||
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