Scaling behavior for finite O(n) systems with long-range interaction

Abstract

A detailed investigation of the scaling properties of the fully finite $\mathcal{O}(n)$ systems with long-range interaction, decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma }$, below their upper critical dimension is presented. The computation of the scaling functions is done to one loop order in the non-zero modes. The results are obtained in an expansion of powers of $\sqrt{\epsilon }$, where $\epsilon =2\sigma -d$ up to $\mathcal{O}({\epsilon }^{3/2})$. The thermodynamic functions are found to be functions the scaling variable $z=R{L}^{2-\eta -\epsilon /2}{U}^{-1/2}$, where $R$ and $U$ are the coupling constants of the constructed effective theory, and $L$ is the linear size of the system. Some simple universal results are obtained.

17 revtex pages, minor correction. new results and references are added

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• Test of renormalization predictions for universal finite-size scaling functions
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Cited by in corpus (4)

• The boundary between long-range and short-range critical behavior
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction
• Critical behavior of systems with long-range interaction in restricted geometry