Physics

Square lattice

Degeneracy (biology)

Thermal fluctuations

Bioinformatics

Quantum phase transition

Biology

Quantum fluctuation

Quantum critical point

Antiferromagnetism

Acoustics

Thermal

Condensed matter physics

Lattice (music)

Frustration

Ising model

Semiclassical physics

Quantum mechanics

Quantum

Thermodynamics

Physical review. B./Physical review. B

In frustrated magnetic systems with competing interactions fluctuations can lift the residual accidental degeneracy. We argue that the state selection may have different outcomes for quantum and thermal order by disorder. As an example, we consider the semiclassical Heisenberg fcc antiferromagnet with only the nearest-neighbor interactions. Zero-point oscillations select the type 3 collinear antiferromagnetic state at $T=0$. Thermal fluctuations favor instead the type 1 antiferromagnetic structure. The opposite tendencies result in a finite-temperature transition between the two collinear states. Competition between effects of quantum and thermal order by disorder is a general phenomenon and is also realized in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square-lattice antiferromagnet at the critical point ${J}_{2}=\frac{1}{2}{J}_{1}$.

Quantum versus thermal fluctuations in the fcc antiferromagnet: Alternative routes to order by disorder