O'Connor, Denjoe and Santiago, J. A. and Stephens, C. R. (2006) An analytic equation of state for Isinglike models. Journal of Physics A: Mathematical and Theoretical, 40 (5). pp. 901918. ISSN 17518113

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Abstract
Using an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, y = f(x), that exhibits all desired asymptotic and analyticity properties in the three limits x → 0, x → ∞ and x → −1. The only necessary inputs are the Wilson functions γ_λ , γ_φ and γ_(φ^2) , associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the WilsonFisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N = 1, we derive a oneloop equation of state for 2 < d < 4 naturally parameterized by a ratio of nonlinear scaling fields. For d = 3 we show that a nonparameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the oneloop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.
Item Type:  Article 

Divisions:  School of Theoretical Physics > Preprints 
Date Deposited:  05 Oct 2017 19:31 
Last Modified:  16 Jul 2018 09:59 
URI:  http://dair.dias.ie/id/eprint/195 
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