Unification of the nature's complexities via a matrix permanent-critical phenomena, fractals, quantum computing, #p-complexity

Abstract

We reveal the analytic relations between a matrix permanent and major nature's complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions,(ii)polynomials of complex variables,(iii)Laplace integral,and(iv)MacMahon master theorem.