Taroni A, Bramwell ST, Holdsworth PCW. Universal window for two-dimensional critical exponents.
JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008;
20:275233. [PMID:
21694394 DOI:
10.1088/0953-8984/20/27/275233]
[Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Two-dimensional condensed matter is realized in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic physics and chemical detail. To unify their physical description is therefore a complex and important challenge. Here we investigate the distribution of experimentally estimated critical exponents, β, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window ∼0.1≤β≤0.25, facts that are only in partial agreement with the established theory of critical phenomena. In particular, the bounded nature of the distribution is impossible to reconcile with the existing theory for one of the major universality classes of two-dimensional behaviour-the XY model with four-fold crystal field-which predicts a spectrum of non-universal exponents bounded only from below. Through a combination of numerical and renormalization group arguments we resolve the contradiction between theory and experiment and demonstrate how the 'universal window' for critical exponents observed in experiment arises from a competition between marginal operators.
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