紧化$λϕ^4$理论的临界性态
Critical behaviour of the compactified $λϕ^4$ theory
摘要：
研究了$N$分量欧氏$λϕ^4$模型在首阶$\frac{1}{N}$展开式下的临界行为.我们认为它在三种情况下：限制在两个平行的平面之间的距离$L$彼此分开，限制在一个无限长的圆柱体具有正方形横截面面积$A$和体积$V$的立方体盒。以质量项的形式$m_{0}^2=α(T - T_{0})$，我们检索金斯堡-朗道模型，这是应该描述样品的材料经历相变，分别在一个薄膜，一个线和一个晶粒的形式，其体积转变温度（$T_{0}$）是已知的。我们得到的方程的临界温度作为$L$（膜），$A$（线），$V$（粮食）和$T_{0}$的功能，并确定维持过渡的极限尺寸。
英文摘要：
We investigate the critical behaviour of the $N$-component Euclidean $λϕ^4$ model at leading order in $\frac{1}{N}$-expansion. We consider it in three situations: confined between two parallel planes a distance $L$ apart from one another, confined to an infinitely long cylinder having a square cross-section of area $A$ and to a cubic box of volume $V$. Taking the mass term in the form $m_{0}^2=α(T - T_{0})$, we retrieve Ginzburg-Landau models which are supposed to describe samples of a material undergoing a phase transition, respectively in the form of a film, a wire and of a grain, whose bulk transition temperature ($T_{0}$) is known. We obtain equations for the critical temperature as functions of $L$ (film), $A$ (wire), $V$ (grain) and of $T_{0}$, and determine the limiting sizes sustaining the transition.
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