An ab initio Calculation of the Universal Equation of State for the O(N) Model

Details An ab initio Calculation of the Universal Equation of State for the O(N) Model An ab initio Calculation of the Universal Equation of State for the O(N) Model

2008-11-13

arxiv.org/abs/0811.2202v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, to appear in Journal of Physics A

Scientific paper

10.1088/1751-8113/42/4/045003

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 $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$ 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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