Citation:Tobias Reinhart, & Gemma De las Cuevas (2022). The grammar of the Ising model: A new complexity hierarchy. 为了探讨Ising模型的复杂性, 一种有效的方法是通过分析其基态能量(Ground State Energy, GSE)问题的复杂性来展开讨论。 具体来说,GSE问题的定义是:给定一个相互作用图和某个能量值k, 判...
Inspired by the potential energy conversion of the springs, we propose the Spring-Ising Algorithm, a point convolutional neural network algorithm for ground state search based on the spring vibration model. Spring-Ising Algorithm regards the spin as a moving mass point connected to a spring and ...
www.nature.com/scientificreports OPEN Point convolutional neural network algorithm for Ising model ground state research based on spring vibration Zhelong Jiang 1,2, Gang Chen 1*, Ruixiu Qiao 1, Pengcheng Feng 1,2, Yihao Chen 1,2, Junjia Su 1,2, Zhiyuan ...
This transition depends on the time Δt during which the adiabatic change occurs and depends on the minimum energy gap between the ground state and the first excited state of the adiabatic process. When applied to the Ising model, we select the initial Hamiltonian H0=∑iXi, describing the ...
ground state (in particlular the S, L, and J quantum numbers is known, the atomic susceptibility can be calculated. The simplest case is again the J = 0 case, where the first term in (5) again vanishes. Then the second term and third term compete, and can result in either a diam...
2.Ground State and Excited States 体系的基态应满足的条件为: \eta _k|G\rangle =0,\forall k 。先讨论 H_{\mathrm{APBC}} ,容易验证基态可以写成以下形式[1]: \begin{equation} \begin{aligned} |G\rangle _{\mathrm{APBC}}&=\prod_{k>0}{\left( u_k+i\nu _kc_{k}^{\...
This paper focuses on the ground state phase diagram of a 1D spin/2 quantum Ising model with competing first and second nearest neighbour interactions known as the axial next nearest neighbour Ising model in the presence of a transverse magnetic field. Here, using quantum correlations, both ...
"Avalanches" in the ground state of the 3D Gaussian random field Ising model driven by an external field We present a numerical study of the exact ground states of the 3D Gaussian random field Ising model (G-RFIM) with an applied external field B. We combine a... C Frontera Beccaria,SE...
weakly periodic ground stateFor the Potts model with competing interactions, we describe the set of weakly periodic ground states corresponding to index-two normal divisors of the Cayley tree group representation. We also study some weakly periodic Gibbs measures....
为了简单起见,第一次notes只会给一些background和first order perturbation的内容。 1.The Hamiltonian. TFIM的哈密顿量可以写为 H=−J(g∑iσix+∑iσizσi+1z) 其中σ 对应泡利矩阵,x自然就是横场项了,负号意味着这是一个所谓的铁磁链。当然,其实你可以通过旋转的方式改变x和z,这是后话。 我们可以...