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Physics Letters A

“Purely” loop renormalizations of the Ginzburg-Landau-Wilson functional as a solution of the thermal conductivity equation

Alexander E. Filippov, Alexander A. Lisyansky

Published Nov 1, 1987• 3 citations
Publisher
DOI
10.1016/0375-9601(87)90155-1

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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→0x\to 0x→0, x→∞x\to\inftyx→∞ and x→−1x\to -1x→−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 γλγ_λγλ​, γϕγ_ϕγϕ​ and γϕ2γ_{ϕ^2}γϕ2​ 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.
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→0x\to 0x→0, x→∞x\to\inftyx→∞ and x→−1x\to -1x→−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 γλγ_λγλ​, γϕγ_ϕγϕ​ and γϕ2γ_{ϕ^2}γϕ2​ 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.