https://doi.org/10.1140/epjs/s11734-023-00971-w
Regular Article
Effective exponents near bicritical points
1
Abrikosov Center for Theoretical Physics, MIPT, Institutsky Lane, 9, 141701, Dolgoprudny, Moscow Region, Russia
2
ITMO University, Kronverkskiy Prospekt 49, 197101, St. Petersburg, Russia
3
School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 6997801, Tel Aviv, Israel
Received:
20
April
2023
Accepted:
22
August
2023
Published online:
4
September
2023
The phase diagram of a system with two order parameters, with 
and 
components, respectively, contains two phases, in which these order parameters are non-zero. Experimentally and numerically, these phases are often separated by a first-order “flop” line, which ends at a bicritical point. For 
and 
dimensions (relevant, e.g., to the uniaxial antiferromagnet in a uniform magnetic field), this bicritical point is found to exhibit a crossover from the isotropic n-component universal critical behavior to a fluctuation-driven first-order transition, asymptotically turning into a triple point. Using a novel expansion of the renormalization group recursion relations near the isotropic fixed point, combined with a resummation of the sixth-order diagrammatic expansions of the coefficients in this expansion, we show that the above crossover is slow, explaining the apparently observed second-order transition. However, the effective critical exponents near that transition, which are calculated here, vary strongly as the triple point is approached.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjs/s11734-023-00971-w.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
