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Loops arises as long length description for many quantum problems, in particular for SU(n) magnets. An interesting scenario in this kind of problems is the so-called deconfined criticality, a transition between Néel and valence bond solid phases in 2D quantum magnets, where numerical studies support a continuous phase transition but also display strong violations of finite size scaling that are not yet understood. This scenario is also believed to describe the phase transition for classical magnets where hedgehogs are suppressed. Three dimensional completely-packed loop models were shown to describe the same features as quantum magnets in 2D and the phase transition between a Néel state and a valence bond liquid. By modifying these loop models we can drive them to a phase transition with the same features: a magnetic ordered phase where there are long loops and a paramagnetic phase where a lattice symmetry is broken. In common with the direct studies of quantum Hamiltonians, we find strong violations of scaling for the SU(2) case. We describe accurately these violations and reach larger sizes than previous studies, making use of a wide range of observables. However, we do not find any conventional signs of a first order transition.

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Pablo Serna Martinez, Universidad de Murcia
Seminarraum Theoretische Physik
Contact: Simon Trebst