梅爾曼–瓦格納定理
外觀
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在量子場論和統計力學中,梅爾曼–瓦格納定理(Mermin–Wagner定理,或稱梅爾銘-瓦格納-霍亨貝格定理、梅爾銘-瓦格納-別列津斯基定理、科勒曼定理)闡述了維度d ≤ 2的場論沒有自發對稱破缺(要不然無質量的南部玻色子會有無限的相關函數)。
概覽
[編輯]若 φ 是高斯自由場(一種純量場),m是質量,維度d=2;傳播子是:
若m=0,
因為高斯定律,
若,,所以一維或二維的純量場沒有明確定義的平均值。
參見墨西哥帽模型。
XY模型的相變
[編輯]d=2的O(2)模型沒有自發對稱破缺,但是有別列津斯基-科斯特利茨-索利斯相變。
(量子相變不受影響。)
兩相是:
1、
2、冪定律
(a ≪ r ≪ ξ
a 是晶格常數
歷史
[編輯]限制
[編輯]參考文獻
[編輯]- ^ see Cardy (2002)
- ^ See Gelfert & Nolting (2001) .
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