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

O'Connor, Denjoe, Santiago, J. A. and Stephens, C. R. (2008) An ab initio Calculation of the Universal Equation of State for the O(N) Model. Journal of Physics A: Mathematical and Theoretical, 42 (4). 045003. ISSN 1751-8113

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Official URL: http://doi.org/10.1088/1751-8113/42/4/045003

Abstract

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 → 0, x → ∞ and x → −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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:19
Last Modified: 15 Dec 2022 08:54
Identification Number: DIAS-STP-08-25
URI: https://dair.dias.ie/id/eprint/233

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