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Register a new userFluctuation-dominated phase ordering at a mixed order transition
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Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.
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We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions which exhibits a mixed order transition (MOT), namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models which are seemingly unrelated. The model we present serves as a link between two classes of models which exhibit MOT in one dimension, namely, spin models with a coupling constant which decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained a lot of attraction since their implementation in the context of driven-open quantum systems represents a viable possibility to engineer unique, pure states. In this work, we analyze a driven many-body spin system, which undergoes a transition from a dark steady state to a mixed steady state as a function of the driving strength. This transition connects a zero entropy (dark) state with a finite entropy (mixed) state and thus goes beyond the realm of equilibrium statistical mechanics and becomes of genuine nonequilibrium character. We analyze the relevant long wavelength fluctuations driving this transition in a regime where the system performs a discontinuous jump from a dark to a mixed state by means of the renormalization group. This allows us to approach the nonequilibrium dark state transition and identify similarities and clear differences to common, equilibrium phase transitions, and to establish the phenomenology for a first order dark state phase transition.
The Verwey phase transition in magnetite is analyzed on the basis of the Landau theory. The free energy functional is expanded in a series of components belonging to the primary and secondary order parameters. A low-temperature phase with the monoclinic P2/c symmetry is a result of condensation of two order parameters X_3 and Delta_5 . The temperature dependence of the shear elastic constant C_44 is derived and the mechanism of its softening is discussed.
We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219 (2000)], we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.
Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far from thermal equilibrium. In a recent paper [1] an exactly soluble spin model with long-range interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to lay a bridge between two classes of one dimensional models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper we elaborate on the calculations done in [1]. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins, and also consider a broader class of interactions which decay with distance with a power law different from 2.
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