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Phase Structures of Field Thoeries with Topological Term

拓扑项场论的相结构

基本信息

批准号：
07640417
负责人：
YONEYAMA Hiroshi
金额：
$ 0.9万
依托单位：
Saga University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640417/
关键词：
Lattice gauge theory Topological term Phase Structure Monte Carlo simulation Real space renormalization group Topological charge Fixed point action 場の理論トポロジーシ-タ真空相転移実空間くりこみ群

项目摘要

Phase structures of lattice field theories with topological term are studied by means of (1) Monte Carlo (MC) simulations as well as (2) real space renormalization group (RSRG) method. (1) In MC study, the notorious problem of the complex Boltzmann weights due to the complex action of the topological term is overcome by calculating the topological charge distribution P (Q). The partition function is calculated by fourier transforming P (Q). CP^1 model is studied for two cases ; (i) standard action and (ii) fixed point (EP) action. (i) In the strong coupling regions, P (Q) behaves as gaussian with the exponent proportional to 1/V (V : volume of the system). This turns out to show the first order phase transition at rheta=pi. In the weak coupling regions, the transition disappears. In the beta-rheta plane no other signatures of phase transitions are found. (ii) In the case of the FP action, this 1st order phase transition occurs only at rheta=pi in the strong coupling limit.(2) RSRG study has applied to (i) U (1) and (ii) U (2) gauge models in two dimensions. Irreducible character expansions are useful in order to obtain the closed form of the RG equation. (i) In U (1) case, the non trivial infrared (IR) fixed point appears besides the IR fixed point at the strong coupling limit. P (Q) is calculated analytically and shows the gaussian behavior. For any value of the coupling constant, the model undergoes the 1st. order phase transition at rheta=pi. This agrees with the results of MC simulations. (ii) In U (2) case, model with the Wilson real action and the standard imaginary action (abelian) is studied. Non-trivial IR fixed point appears at rheta=pi as in the case (i). For rheta*pi, successive RG transformations induce the non-abelian representations in the imaginary part of the action. But these trajectories end up with the IR fixed point at beta=0.

利用Monte Carlo（MC）模拟和真实的空间重整化群（RSRG）方法研究了含拓扑项的格点场论的相结构。(1)在MC研究中，通过计算拓扑电荷分布P（Q）克服了由于拓扑项的复杂作用而导致的复杂Boltzmann权重的臭名昭著的问题。通过傅立叶变换P（Q）计算配分函数。CP^1模型研究了两种情况：（i）标准作用和（ii）不动点（EP）作用。(i)在强耦合区，P（Q）表现为高斯型，其指数与1/V（V：系统体积）成正比。这证明了在reta =pi处的一级相变。在弱耦合区，跃迁消失。在β-rheta平面没有发现其他的相变的签名。（ii）在FP行动的情况下，这种第一阶相变只发生在rheta= π在强耦合限制。(2)RSRG研究应用于二维U（1）和U（2）规范模型。为了得到RG方程的封闭形式，不可约特征展开是有用的。(i)在U（1）情形下，在强耦合极限下，除了红外不动点外，还出现了非平凡的红外不动点。P（Q）是解析计算的，并显示高斯行为。对于耦合常数的任何值，该模型经历第一。在reta = π.这与MC模拟的结果一致。(ii)在U（2）情形下，研究了具有Wilson真实的作用量和标准虚作用量（阿贝尔作用量）的模型.非平凡IR不动点出现在reta =pi处，如在情况（i）中。对于rheta*pi，连续的RG变换在作用量的虚部中诱导出非阿贝尔表示。但是这些轨迹最终以β =0的IR固定点结束。