Effective exponents near bicritical points

TL;DR

This paper investigates the critical behavior near bicritical points in systems with two order parameters, revealing a slow crossover from isotropic criticality to a fluctuation-driven first-order transition and analyzing the variation of effective exponents.

Contribution

The authors introduce a novel renormalization group expansion and resummation technique to analyze the crossover behavior near bicritical points in three-dimensional systems.

Findings

Crossover from isotropic criticality to first-order transition is slow.

Effective critical exponents vary strongly near the triple point.

Second-order transition appears despite underlying fluctuation-driven first-order behavior.

Abstract

The phase diagram of a system with two order parameters, with ${\it n_1}$ and $n_2$ 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 $n=n_1+n_2=3$ and $d=3$ 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.