Mathematical Sciences: Quantum Mechanical Classical Lattice Spin Systems

在这个项目中，主要研究者将研究 在Halfonite相和二聚体之间的相变 自旋为1的海森堡反铁磁相，一维 量子自旋系统 特别是，他将证明， 相变确实存在，这表明一种有序- 为这种转变提出的参数在一个阶段为零， 另一个为非零。 此外，首席研究员 将继续他对多数决原则的严格研究 Ising型系统的重整化群变换 最后，他将研究连续谱的存在性， 量子自旋哈密顿量的无限体积极限 系统 物质在微观尺度上的行为非常 决定物质宏观行为的因素 或日常生活中可观察到的尺度。 例如，我们称之为 液体或气体的温度仅仅是宏观的， 无数原子和分子运动的累积效应 在材料的微观尺度上。 本工程 首席研究员将研究各种数学模型， 原子在微观或量子水平上的行为， 为了建立微观和微观之间的联系， 物质的宏观性质。

In this project the principal investigator will study the phase transition between the Haldane phase and the dimerized phase in the spin-1 Heisenberg antiferromagnetic, one-dimensional quantum spin system. In particular, he will prove that this phase transition does indeed exist by showing that an order- parameter proposed for this transition is zero in one phase and nonzero in the other. In addition, the principal investigator will continue his rigorous study of the majority rule renormalization group transformation for Ising-type systems. Finally he will study the existence of continuous spectra for the infinite volume limit of the Hamiltonian of a quantum spin system. The behavior of matter at the microscopic scale is very often what determines the behavior of matter at the macroscopic or observable scales of ordinary life. For example, what we call the temperature of a liquid or gas is simply the macroscopic or cumulative effect of the motion of countless atoms and molecules on the microscopic scale of the material. In this project the principal investigator will study various mathematical models of the behavior of atoms at the microscopic or quantum level, in order to establish connections between microscopic and macroscopic properties of matter.