Thus, it may be confusing to refer to the transition driven by topological defectsĪs a topological phase transitions, since the appearance of topological defectsĭecrease the chance to produce topological phases of matter. If we refer to phase transitions induced by topological defects as topological phase transitions, and refer to phase transitions between different. Topological phase transitions, nor are topological phase transitions topological phase transitions. While transitions driven by fluctuations without any topological defects usually produce disordered states that have non-trivial topological orders, and correspond to topological phase transitions. In general topological phase transitions are not Topological orders as topological phase transitions, then our result can If we refer to phase transitions induced by topological defects as topological phase transitions, and refer to phase transitions between different Orders, and correspond to topological phase transitions. While transitions driven by fluctuations without any topologicalĭefects usually produce disordered states that have non-trivial topological That have no topological order, and correspond to non-topological phase In this paper, we show that the phase transitions driven byįluctuations with all possible topological defects produce disordered states 1Mean-field formulation (no long-range correlation) Toggle Mean-field formulation (no long-range correlation) subsection 1.1Second-order transitions 1. The importance of the topological defects in phase transitions have been emphasized by Kosterlitz and Thouless, who shared 2016 Nobel prize (with Haldane) ``for theoretical discoveries of topological phase transitions and topological phases of matter''. We like to ask if the disordered phase has topological order or not. One should also mention that there are several statistical mechanical models in which the phase transition can be understood as the percolation transition of a suitable (dependent) percolation model. Let us consider a quantum phase transition (at T=0) from an ordered phase to a disordered phase, driven by the quantum fluctuations of the order parameter.
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