Wu Yantao, Car Roberto
The Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
The Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2020 Nov 6;125(19):190601. doi: 10.1103/PhysRevLett.125.190601.
We extend to quenched-disordered systems the variational scheme for real-space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two- and three-dimensional lattices.
我们将最近为均匀自旋哈密顿量引入的实空间重整化群计算的变分方案扩展到淬火无序系统。当存在无序时，我们的方法可以得到重整化哈密顿量分布的流，从中如果重整化耦合的相关性保持有限范围，就可以计算临界指数。变分方法的关键是通过在统计力学中最小化一个凸泛函找到的偏差势。这个势极大地减少了大无序系统中的蒙特卡罗弛豫时间。我们通过将该方法应用于二维稀释伊辛模型、随机横向场量子伊辛链以及二维和三维晶格中的随机场伊辛模型来证明该方法。
