The enigmatic exponent koppa and the story of finite-size scaling above the upper critical dimension

Ralph Kenna; Bertrand Berche

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arXiv · 2404.09191

The enigmatic exponent koppa and the story of finite-size scaling above the upper critical dimension

Ralph Kenna·Bertrand Berche

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Abstract

Scaling, hyperscaling and finite-size scaling were long considered problematic in theories of critical phenomena in high dimensions. The scaling relations themselves form a model-independent structure that any model-specific theory must adhere to, and they are accounted for by the simple principle of homogeneity. Finite-size scaling is similarly founded on the fundamental idea that only two length scales enter the game -- namely system length and correlation length. While all scaling relations are quite satisfactory for multitudes of physical systems in low dimensions, one fails in high dimensions...

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Ralph Kenna, Bertrand Berche. 2024-04-14. The enigmatic exponent koppa and the story of finite-size scaling above the upper critical dimension. https://arxiv.org/abs/2404.09191

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