Search Results (5 total)

We determine the Poisson ratio of self-avoiding fixed-connectivity membranes, modeled as impenetrable plaquettes, to be σ  =  -0.37(6), in statistical agreement with the Poisson ratio of phantom fixed-connectivity membranes σ  =  -0.32(4). Together with the equality of critical exponents, this result implies a unique universality class for fixed-connectivity membranes. Our findings thus establish that physical fixed-connectivity membranes provide a wide class of auxetic (negative Poisson ratio) materials with significant potential applications in materials science.

We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to the combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set of five distinct vertices, we allow triangulations containing multiply connected simplexes and distinct simplexes defined by the same set of vertices. We demonstrate numerically that including degenerated triangulations substantially reduces the finite-size effects in the model. In particular, we provide strong numerical evidence for an exponential bound on the entropic growth of the ensemble of degenerate triangulations, and show that a discontinuous crumpling transition is already observed on triangulations of volume N₄≈4000.

We provide the first numerical evidence for the existence of a tubular phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes without self-avoidance. Incorporating anisotropy into the bending rigidity of a simple model of a tethered membrane with free boundary conditions, we show that the model indeed has two phase transitions corresponding to the flat-to-tubular and tubular-to-crumpled transitions. For the tubular phase we measure the Flory exponent ν_F and the roughness exponent ζ. We find ν_F  =  0.305(14) and ζ  =  0.895(60), which are in reasonable agreement with the theoretical predictions of RT; ν_F  =  1/4 and ζ  =  1.

A modified Wilson action which suppresses plaquettes which take negative values is used to study the scaling behavior of the string tension. The use of the β_E scheme gives good agreement with asymptotic two loop results.

Under certain conditions, the renormalization-group flow of models in statistical mechanics can change dramatically under just very small changes of given external parameters. This can typically occur close to bifurcations of fixed points, close to the complete disappearance of fixed points, or in regions where the renormalization-group flow becomes chaotic. We present some explicit examples of these phenomena for the case of a Lie group valued spin-model analyzed by means of a variational real-space renormalization group. By directly computing the free energy of these models around the parameter regions in which such nontrivial modifications of the renormalization-group flow occur, we can extract the physical consequences of these phenomena.