Development of a (4–ε)-dimensional theory for the density of states of a disordered system near the Anderson transition

摘要: The calculation of the density states for Schrodinger equation with a Gaussian random potential is equivalent to problem second-order transition 'wrong' sign coefficient quartic term in Ginzburg–Landau Hamiltonian. special role dimension d = 4 such Hamiltonian can be seen from different viewpoints but fundamentally determined by renormalizability theory. construction an e expansion direct analogy phase-transition theory gives rise 'spurious' pole. To solve this problem, proper treatment factorial divergency perturbation series necessary. Simplifications arising high dimensions used development (4–e)-dimensional theory, requires successive consideration four types theories: nonrenormalizable theories > 4, and renormalizable logarithmic situation (d 4), super-renormalizable < 4. An approximation found each type giving asymptotically exact results. In terms leading order 1/e are only retained N~1 (N theory) while all degrees essential large N view fast growth their coefficients. latter calculated Callan–Symanzik results Lipatov method as boundary conditions. qualitative effect same cases consists shifting phase point complex plane. This elimination pole regularity energies. A discussion given orders perspective conductivity near Anderson transition.