Experimental evidence for the existence of strictly higher-order phase transitions (of order three or above in the Ehrenfest sense) is tenuous at best. However, there is no known physical reason why such transitions should not exist in nature. Here, higher-order transitions characterized by both discontinuities and divergences are analysed through the medium of partition function zeros. Properties of the distributions of zeros are derived, certain scaling relations are recovered, and new ones are presented.
Bibliographical noteThe full text is also available from: http://de.arxiv.org/abs/cond-mat/0512352
NOTICE: this is the author’s version of a work that was accepted for publication in Nuclear Physics B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nuclear Physics B, [736, 3, 2006] DOI: 10.1016/j.nuclphysb.2005.12.013.
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