2,183 research outputs found

    Potts Model On Random Trees

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    We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a previous approach are made, showing where its assumption of uniform local fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure

    Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons

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    We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schroedinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions

    BKT-like transition in the Potts model on an inhomogeneous annealed network

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    We solve the ferromagnetic q-state Potts model on an inhomogeneous annealed network which mimics a random recursive graph. We find that this system has the inverted Berezinskii--Kosterlitz--Thouless (BKT) phase transition for any q≥1q \geq 1, including the values q≥3q \geq 3, where the Potts model normally shows a first order phase transition. We obtain the temperature dependences of the order parameter, specific heat, and susceptibility demonstrating features typical for the BKT transition. We show that in the entire normal phase, both the distribution of a linear response to an applied local field and the distribution of spin-spin correlations have a critical, i.e. power-law, form.Comment: 7 pages, 3 figure

    Half the entanglement in critical systems is distillable from a single specimen

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    We establish that the leading critical scaling of the single-copy entanglement is exactly one half of the entropy of entanglement of a block in critical infinite spin chains in a general setting, using methods of conformal field theory. Conformal symmetry imposes that the single-copy entanglement for critical many-body systems scales as E_1(\rho_L)=(c/6) \log L- (c/6) (\pi^2/\log L) + O(1/L), where L is the number of constituents in a block of an infinite chain and c corresponds to the central charge. This proves that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to general isotropic quasi-free fermionic models. An analytic example of the XY model shows that away from criticality the above simple relation is only maintained near the quantum phase transition point.Comment: 4 pages RevTeX, 1 figure, final versio

    Phenomenological Models of Socio-Economic Network Dynamics

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    We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.Comment: 11 pages, 8 figure

    Correlations in interacting systems with a network topology

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    We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance â„“\ell, decay, on average, faster than 1/(â„“zâ„“)1/(\ell z_\ell). Here zâ„“z_\ell is the mean number of the â„“\ell-th nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number z2z_2 in the infinite network limit. In this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach.Comment: 5 page

    The Lovastatin-Treated Rodent: A New Model of Barrier Disruption and Epidermal Hyperplasia

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    Recent studies have linked epidermal cholesterol synthesis with maintenance of the permeability barrier. To assess directly the importance of cholesterol synthesis, we applied lovastatin, a potent inhibitor of cholesterol synthesis, to hairless mouse skin. Transepidermal water loss (TEWL) began to increase after four to six daily applications. Co-application of cholesterol blocked the expected increase in TEWL, demonstrating the importance of cholesterol for development of the lesion. The histology of lovastatin-treated skin revealed epidermal hyperplasia, accompanied by accelerated DNA synthesis. Whereas cholesterol synthesis initially was reduced in lovastatin-treated epidermis, with further treatment cholesterol synthesis normalized, while fatty acid synthesis accelerated greatly. Although the total free sterol content of lovastatin-treated epidermis remained normal, the fatty acid content increased coincident with barrier disruption. Finally, morphologic abnormalities of both lamellar body structure and their deposited, intercellular contents occurred coincident with the emerging biochemical abnormalities. Thus, the abnormal barrier function in this model can be ascribed to an initial inhibition of epidermal sterol synthesis followed by an alteration in cholesterol and fatty acid synthesis, leading to an imbalance in stratum corneum lipid composition and abnormal membrane bilayer structure
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