标题： 三维伊辛模型的降维数值研究 显示英文标题

标题： Numerical study of the dimensionally reduced 3D Ising model

摘要： 我们通过数值模拟研究无限体积极限下的三维伊辛模型$N_{x,y,z}\to\infty$。 我们确定了$T_c$以及临界指数$\beta,\gamma$和$\nu$，基于有限尺寸标度和直方图重加权技术。 此外，我们研究了一个“维度降低”的情景，其中$N_z$被固定（例如，取 2、4、8），同时取极限$N_{x,y}\to\infty$。 对于每个固定的$N_z$，我们确定$T_c$以及$\beta,\gamma,\nu$。 对于$T_c$，我们找到一条平滑的过渡曲线，该曲线连接了二维和三维伊辛模型已知的临界温度。 关于$\beta,\gamma,\nu$，我们的数据表明，无论$N_z$如何，"维度减少"的伊辛模型与二维伊辛模型处于同一普适性类中。 显示英文摘要

摘要： 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 $\beta,\gamma$ and $\nu$, 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 $\beta,\gamma,\nu$. 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 $\beta,\gamma,\nu$ our data suggest that the ``dimensionally reduced'' Ising model is in the same universality class as the 2D Ising model, regardless of $N_z$.