Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

Emilio Jose Flores Sola, Bertrand Berche, R. kenna, M. Weigel

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Abstract

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour by simulating one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.
Original languageEnglish
Pages (from-to)1-8
JournalThe European Physical Journal B
Volume88
Issue number1
DOIs
Publication statusPublished - Jan 2015

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Ising model
Linear systems
Phase transitions
scaling
interactions
linear systems
breakdown

Keywords

  • Statistical and Nonlinear Physics

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Finite-size scaling above the upper critical dimension in Ising models with long-range interactions. / Flores Sola, Emilio Jose; Berche, Bertrand; kenna, R.; Weigel, M.

In: The European Physical Journal B, Vol. 88, No. 1, 01.2015, p. 1-8.

Research output: Contribution to journalArticle

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