Numerical study of the dimensionally reduced 3D Ising model

Abstract

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 ${\hat{I}}^2,{\hat{I}}^3$ and $\hat{I}½$, 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 ${\hat{I}}^2,{\hat{I}}^3,\hat{I}½$. 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 ${\hat{I}}^2,{\hat{I}}^3,\hat{I}½$ our data suggest that the ``dimensionally reduced'' Ising model is in the same universality class as the 2D Ising model, regardless of $N_z$.

8 pages, 6 figures, 1 table. Proceedings of the 41st International Symposium on Lattice Field Theory (LATTICE2024), 28 July - 3 August 2024, Liverpool, UK