O（N）模型通用状态方程的从头计算
An ab initio Calculation of the Universal Equation of State for the O(N) Model
摘要：
利用环境友好重整化群我们导出了O（N）模型y=f（x）的状态方程的从头算普适标度形式，它在$x\to 0$，$x\to\infty$和$x\to -1$的极限范围内具有所有必需的解析性质.与目前基于唯象标度分析的方法不同，标度函数仅从底层Landau-Ginzburg-Wilson Hamilton导出，并且仅依赖于三个Wilson函数$γ_λ$、$γ_ϕ$和$γ_{ϕ^2}$，这三个Wilson函数在Wilson-Fisher不动点和与共存曲线上的Goldstone模式相关联的强耦合不动点之间表现出非平凡的交叉。我们给出了N=2，3和4到单圈阶的显式结果，并与已知结果进行了比较。
英文摘要：
Using an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y=f(x), that exhibits all required analyticity properties in the limits $x\to 0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on a phenomenological scaling ansatz the scaling function is derived solely from the underlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the three Wilson functions $γ_λ$, $γ_ϕ$ and $γ_{ϕ^2}$ which exhibit a non-trivial crossover between the Wilson-Fisher fixed point and the strong coupling fixed point associated with the Goldstone modes on the coexistence curve. We give explicit results for N=2, 3 and 4 to one-loop order and compare with known results.
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