Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

An Observation on the Experimental Measurement of Dislocation Density

The common practice of ignoring the elastic strain gradient in measurements of geometrically necessary dislocation (GND) density is critically examined. It is concluded that the practice may result in substantial errors. Our analysis points to the importance of spatial variations of the elastic strain field in relation to its magnitude in inferring estimates of dislocation density from measurements.     

Stability and related results in linear elastodynamics on unbounded regions

Communicated by K. R. Rajagopal     

Some convexity considerations for a two-dimensional traction problem

Summary A rectangular strip, consisting of homogeneous, isotropic, elastic material, is in an equilibrium state of plane stress, due to actions applied to a pair of opposite edges, the remaining pair being traction-free. The convexity of certain cross-sectional measures of stress is established; and a generalized convexity property is also established for one such measure, leading to an explicit decay estimate for the measure in the case of a semi-infinite strip, one end of which is subjected to a self-equilibrated load.     

Modulated phases in Ising models with diluted frustration

A particular class of periodic Ising models with diluted frustration is studied using a simple recursion relation for spinor correlation functions. A modulated phase is found at T = 0 which extends into a modulated paramagnetic phase for finite temperatures. The disorder line at which this latter phase changes into a paramagnetic phase is located. In a study of the ground state excitations of the model contact is made with results known for the ANNNI-model.     

Momentum space renormalization for the sine-Gordon model

A momentum space renormalization is presented for the sine-Gordon model with an arbitrary cut-off function. In contrast to previous work the present method reproduces the slope of the critical line as found from the Kosterlitz renormalization of the equivalent Coulomb gas and is also applicable to the case of a sharp cut-off function.