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Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension

R. Kenna
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Abstract

A finite size scaling theory for the partition function zeros and thermodynamic functions of O(N) phi^4-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with multiplicative logarithmic corrections which are linked to the triviality of the theory. These logarithmic corrections are independent of N for odd thermodynamic quantities and associated zeros and are N dependent for the even ones. Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of phi^4_4-theories for all N.

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R. Kenna. 2004-05-26. Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension. https://doi.org/10.1016/j.nuclphysb.2004.05.012

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