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Thursday, January 21st 2016

3:35 pm:

In most systems that exhibit order at low temperatures, the order occurs in the elementary degrees of freedom such as spin or charge. Prominent examples are magnetic or superconducting states of matter. In contrast, emergent order describes the phenomenon where composite objects such as higher order correlation functions exhibit longer range correlations. This can appear even though the elementary objects remain short-range ordered. One specific example are frustrated magnets, where long-range discrete order in the relative orientation of spins may occur in the absence of magnetic order. This can induce other phase transitions as is the case for the nematic transition in the iron pnictides. In my talk, I will focus on algebraic "critical" correlations of an emergent Z6 clock order parameter in an isotropic Heisenberg antiferromagnet on the windmill lattice, which consists of interpenetrating honeycomb and triangular lattices. This is surprising as the interaction of the Goldstone modes present in Heisenberg systems usually causes the spin-wave stiffness to renormalize to zero on long scales. Here it occurs due to the decoupling of an emergent collective degree of freedom given by the relative phase of spins on different sublattices. We establish this result and the formation of an extended critical phase at intermediate temperatures both using an analytical renormalization group analysis based on the Ricci flow and large-scale classical Monte-Carlo simulations. Our results also reveal that both phase transitions, which bracket the critical phase, lie in the Berezinskii-Kosterlitz-Thouless universality class.

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