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

Fuente: arXiv
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Main Authors: Kenna, Ralph, Berche, Bertrand
Format: Preprint
Published: 2024
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author Kenna, Ralph
Berche, Bertrand
author_facet Kenna, Ralph
Berche, Bertrand
contents 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...
format Preprint
id arxiv_https___arxiv_org_abs_2404_09191
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The enigmatic exponent koppa and the story of finite-size scaling above the upper critical dimension
Kenna, Ralph
Berche, Bertrand
Statistical Mechanics
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...
title The enigmatic exponent koppa and the story of finite-size scaling above the upper critical dimension
topic Statistical Mechanics
url https://arxiv.org/abs/2404.09191