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

Chigak Itoi; Hisamitsu Mukaida

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

Chigak Itoi·Hisamitsu Mukaida

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Abstract

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\uı-Kosterlitz-Thouless transition.

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Chigak Itoi, Hisamitsu Mukaida. 1999-07-01. Renormalization group for renormalization-group equations toward the universality classification of infinite-order phase transitions. https://arxiv.org/abs/cond-mat/9711308

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