论文标题
圆环上离散高斯SOS模型的新二元关系
New duality relation for the Discrete Gaussian SOS model on a torus
论文作者
论文摘要
我们为二维离散高斯模型构建了一种新的二元性。它基于已知的一维二元性和映射，在中国余下定理，$ n \ times m $ torus和$ nm $站点的戒指之间。二元性适用于任意翻译不变的交互潜力$ v（\ mathbf {r}）$之间的高度变量。它导致相互双重电势的$（v，\ widetilde {v}）$，并根据$ \widetildeβ=π^2/β$的温度反转。当$ v（\ mathbf {r}）$是各向异性时，双重性会呈现一个各向异性$ \ widetilde {v} $。尤其是这种情况，对于各向同性最近的邻近潜力是双重的。在热力学限制中，该双重电位显示出根据具有四极角依赖性的平方逆定律的距离衰减。有一对自偶电位$ v^\ star = \ widetilde {v^\ star} $。在自动温度下，$β^\ star = \ widetilde {β^\ star} =π$可以明确计算高度高度相关；它是各向异性的，并以距离分化。
We construct a new duality for two-dimensional Discrete Gaussian models. It is based on a known one-dimensional duality and on a mapping, implied by the Chinese remainder theorem, between the sites of an $N\times M$ torus and those of a ring of $NM$ sites. The duality holds for an arbitrary translation invariant interaction potential $v(\mathbf{r})$ between the height variables on the torus. It leads to pairs $(v,\widetilde{v})$ of mutually dual potentials and to a temperature inversion according to $\widetildeβ=π^2/β$. When $v(\mathbf{r})$ is isotropic, duality renders an anisotropic $\widetilde{v}$. This is the case, in particular, for the potential that is dual to an isotropic nearest-neighbor potential. In the thermodynamic limit this dual potential is shown to decay with distance according to an inverse square law with a quadrupolar angular dependence. There is a single pair of self-dual potentials $v^\star=\widetilde{v^\star}$. At the self-dual temperature $β^\star=\widetilde{β^\star}=π$ the height-height correlation can be calculated explicitly; it is anisotropic and diverges logarithmically with distance.
