1205.1789 (Mei Yin)

A Markov chain approach to renormalization group transformations    [PDF]

Mei Yin

We aim at an explicit characterization of the renormalized Hamiltonian after decimation transformation of a one-dimensional Ising-type Hamiltonian with a nearest-neighbor interaction and a magnetic field term. A Markov chain method is used to verify the well-known conjecture that the eigenvalues of this renormalization transformation about the fixed point bear important information about all six of the critical exponents, which are independent of the blocking factor. This illustrates the universality property of the renormalization group map in this case.

View original: http://arxiv.org/abs/1205.1789