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

2024/04/14 by Ralph Kenna, Bertrand Berche, Kenna, Ralph +1
Computer Science · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2404.09191

openalex publication_date 2024/04/14 · openalex created_date 2024/04/17 · openalex updated_date 2026/07/28

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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