Renormalization group for renormalization-group equations toward the universality classification of infinite-order phase transitions

Details Renormalization group for renormalization-group equations toward the universality classification of infinite-order phase transitions Renormalization group for renormalization-group equations toward the universality classification of infinite-order phase transitions

1997-11-28

arxiv.org/abs/cond-mat/9711308v4

Physics

Condensed Matter

Statistical Mechanics

19 pages, 10 eps figures

Scientific paper

We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method resolves the problem of a vanishing scaling matrix. The exponent is obtained from the maximal eigenvalue of a scaling matrix in this renormalization group, as in the case of ordinary second-order phase transitions. We exhibit several nontrivial universality classes in infinite-order transitions different from the well-known Berezinski\u\i-Kosterlitz-Thouless transition.

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