论文标题
引导晶格上的伊辛模型
Bootstrapping the Ising Model on the Lattice
论文作者
论文摘要
我们使用Bootstrap方法研究了无限晶格上自旋的统计模型，该方法结合了旋转窗帘身份与阳性条件（包括反射阳性和Griffiths不平等），从而通过半额定式编程在旋转相关器上得出严格的两侧界限。对于平方晶格上的2D ISING模型，基于13个地点钻石区域支持的相关器的引导界确定了与小窗口内的最近的自旋相关器，对于较宽的耦合和磁场而言，它比使用Monte Carlo方法可以窄的耦合和磁场要窄。我们还报告了Cubic晶格上3D ISING模型的引导界限的初步结果。
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous two-sided bounds on spin correlators through semi-definite programming. For the 2D Ising model on the square lattice, the bootstrap bounds based on correlators supported in a 13-site diamond-shaped region determine the nearest-spin correlator to within a small window, which for a wide range of coupling and magnetic field is narrower than the precision attainable with Monte Carlo methods. We also report preliminary results of the bootstrap bounds for the 3D Ising model on the cubic lattice.
