Remarks on the large-N CP(N－1) model
Remarks on the large-N CP(N－1) model
复制标题
大N CP(N-1)模型备注
DOI：
10.1103/physrevd.102.025004
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发表时间：
2020
影响因子：
5
通讯作者：
Antonino Flachi
中科院分区：
文献类型：
--
作者：
山崎 敦;村上 豪;吉岡 和夫;木村 智樹;土屋 史紀;鍵谷 将人;坂野井 健;寺田 直樹;笠羽 康正;吉川 一朗;ひさき（SPRINT-A） プロジェクトチーム;Antonino Flachi
在本文中，我们考虑将模型限制在有限温度和化学势下的有限尺寸区间。我们在大近似中获得了与量子涨落有效质量相关的序参数的单环有效作用的混合梯度展开。这种展开给出了热力学势密度作为阶次参数的函数的表达式，将先前的计算推广到任意大阶和有限化学势的情况，并允许人们讨论模型基态的一些通用特征。这里使用的技术依赖于解析正则化，并提供了一种有效的方案来提取展开系数。一旦知道基态的解，这些系数就可以用来推断基态的一些通用属性作为外部条件的函数。我们还表明，对于所考虑的外部条件的任何值，都不可能过渡到无质量相，并澄清了一个看似重要的观点，即与对数散度的出现和 Mermin-Wagner-Hoenberg-Coleman 定理相关的有效作用的正则化。
In this paper we consider themodel confined to an interval of finite size at finite temperature and chemical potential. We obtain, in the large-approximation, a mixed-gradient expansion of the one-loop effective action of the order parameter associated with the effective mass of the quantum fluctuations. This expansion gives an expression for the thermodynamic potential density as a functional of the order parameter, generalizing previous calculations to arbitrarily large order and to the case of finite chemical potential and allows one to discuss some generic features of the ground state of the model. The technique used here relies on analytic regularization and provides an efficient scheme to extract the coefficients of the expansion. Once a solution for the ground state is known these coefficients can be used to deduce some generic properties of the ground state as a function of external conditions. We also show that there can be no transition to a massless phase for any value of the external conditions considered and clarify a seemingly important point regarding the regularization of the effective action connected to the appearance of logarithmic divergences and to the Mermin-Wagner-Hoenberg-Coleman theorem.