Effective exponents near bicritical points
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
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.
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