Why are tensor field theories asymptotically free?

In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop.Comment: 8 pages, 3 figure

Degenerate Mobilities in Phase Field Models are Insufficient to Capture Surface Diffusion

Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via surface diffusion is the long-time, sharp interface limit of microscopic phase field models such as the Cahn-Hilliard equation with a degenerate mobility function. Contrary to this conventional wisdom, we show that the long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free energy undergoes coarsening, reflecting the presence of bulk diffusion, rather than pure surface diffusion. This reveals an important limitation of phase field models that are frequently used to model surface diffusion

Phase transition of compartmentalized surface models

Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation transition. The first model is a fluid surface one. The vertices can freely diffuse only inside the compartments, and they are prohibited from the free diffusion over the surface due to the domain boundaries. The second is a skeleton model. The surface shape of the skeleton model is maintained only by the domain boundaries, which are linear chains with rigid junctions. Therefore, we can conclude that the first-order transitions occur independent of whether the shape of surface is mechanically maintained by the skeleton (= the domain boundary) or by the surface itself.Comment: 10 pages with 16 figure

Parabolic free boundary price formation models under market size fluctuations

In this paper we propose an extension of the Lasry-Lions price formation model which includes fluctuations of the numbers of buyers and vendors. We analyze the model in the case of deterministic and stochastic market size fluctuations and present results on the long time asymptotic behavior and numerical evidence and conjectures on periodic, almost periodic and stochastic fluctuations. The numerical simulations extend the theoretical statements and give further insights into price formation dynamics

Massless Wigner particles in conformal field theory are free

We show that in a four dimensional conformal Haag-Kastler net, its massless particle spectrum is generated by a free field subnet. If the massless particle spectrum is scalar, then the free field subnet decouples as a tensor product component.Comment: 25 pages, 3 Tikz figures. The final version is available under Open Acces

Structure and Thermodynamical Properties of Zirconium hydrides from first-principle

Zirconium alloys are used as nuclear fuel cladding material due to their mechanical and corrosion resistant properties together with their favorable cross-section for neutron scattering. At running conditions, however, there will be an increase of hydrogen in the vicinity of the cladding surface at the water side of the fuel. The hydrogen will diffuse into the cladding material and at certain conditions, such as lower temperatures and external load, hydrides will precipitate out in the material and cause well known embrittlement, blistering and other unwanted effects. Using phase-field methods it is now possible to model precipitation build-up in metals, for example as a function of hydrogen concentration, temperature and external load, but the technique relies on input of parameters, such as the formation energy of the hydrides and matrix. To that end, we have computed, using the density functional theory (DFT) code GPAW, the latent heat of fusion as well as solved the crystal structure for three zirconium hydride polymorphs: \delta-ZrH1.6, \gamma-ZrH, and \epsilon-ZrH2.Comment: 9 pages, 9 figures, 15th Int. Conf. Environmental Degradation of Materials in Nuclear Power Systems-water reactors Uses graficx, subfigure, threeparttable (2012