Superconductive percolation: Transmission of order by two kinds of poles, zeros and critical fluctuations

Abstract

We present some exact results of the Percolation dynamic critical phenomena, obtained numerically from the distribution functions of the kinetic coefficients such as conductivity, the Hall and Seebeck coefficients and elastic moduli. We introduce two types of the singularity (saddle points) specifically for disordered systems as a function of concentration p, find their location in a real space and show how they ‘grow’ (the poles) and ‘die’ (become the zeros) but their sum remains constant. The number of poles given by N(p) ∝ (p – p _c) ^dv. their fractal dimension given by d _poles = 0 and the negative critical exponent given by k = μ – dv, where μ is the critical exponent of the kinetic coefficient. are obtained. This allows us to present a new picture of ‘propagation of order’ with a dynamic scaling region, consisting of component 1 and component 2, which are interchanged; the poles convert into the zeros, which again become the poles when the critical point is crossed. The critical fluctuations are the result of interchanges of poles into zeros and vice versa. We consider the local poles (zeros) for conductivity and scalar elasticity and the non-local poles (zeros) for the Hall and Seebeck coefficients and vector elasticity, which lead to two types of critical fluctuation: jumps (the scalar forces) and microrotations (the vector forces).