Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2412.04278 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910728765571072 |
|---|---|
| author | Kiel, Tolga Durr, Stephan |
| author_facet | Kiel, Tolga Durr, Stephan |
| contents | We study the 3D Ising model in the infinite volume limit $N_{x,y,z}\to\infty$ by means of numerical simulations. We determine $T_c$ as well as the critical exponents $β,γ$ and $ν$, based on finite-size scaling and histogram reweighting techniques. In addition, we study a ``dimensionally reduced'' scenario where $N_z$ is kept fixed (e.g. at 2, 4, 8), while the limit $N_{x,y}\to\infty$ is taken. For each fixed $N_z$ we determine $T_c$ as well as $β,γ,ν$. For $T_c$ we find a smooth transition curve which connects the well known critical temperatures of the 2D and the 3D Ising model. Regarding $β,γ,ν$ our data suggest that the ``dimensionally reduced'' Ising model is in the same universality class as the 2D Ising model, regardless of $N_z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical study of the dimensionally reduced 3D Ising model Kiel, Tolga Durr, Stephan High Energy Physics - Lattice Statistical Mechanics We study the 3D Ising model in the infinite volume limit $N_{x,y,z}\to\infty$ by means of numerical simulations. We determine $T_c$ as well as the critical exponents $β,γ$ and $ν$, based on finite-size scaling and histogram reweighting techniques. In addition, we study a ``dimensionally reduced'' scenario where $N_z$ is kept fixed (e.g. at 2, 4, 8), while the limit $N_{x,y}\to\infty$ is taken. For each fixed $N_z$ we determine $T_c$ as well as $β,γ,ν$. For $T_c$ we find a smooth transition curve which connects the well known critical temperatures of the 2D and the 3D Ising model. Regarding $β,γ,ν$ our data suggest that the ``dimensionally reduced'' Ising model is in the same universality class as the 2D Ising model, regardless of $N_z$. |
| title | Numerical study of the dimensionally reduced 3D Ising model |
| topic | High Energy Physics - Lattice Statistical Mechanics |
| url | https://arxiv.org/abs/2412.04278 |