New algorithm of numerical functional renormalization group method

Martin Andersson

Noriko Akutsu, Yuko Akutsu

We present a new method for the numerical calculation of the equilibrium crystal shape around a facet. Our method is based on the transfer matrix method with the product-wave-function renormalization group (PWFRG) algorithm for the asymmetric density matrix, which is an extension of the density matrix renormalization group (DMRG) algorithm. By applying this method to the staggered body-centered-cubic solid-on-solid model, which is known to exhibit the inverse roughening phenomena, we obtain the facet shape, shape exponents, and step tension.

Tomotoshi Nishino, Kouichi Okunishi

The authors propose a fast numerical renormalization group method --- the product wave function renormalization group (PWFRG) method --- for 1D quantum lattice models and 2D classical ones. A variational wave function, which is expressed by a matrix product, is improved through a self-consistent calculation. The new method has the same fixed point as the density matrix renormalization group method.

Simone Montangero

Rajan Gupta, Kenneth Geddes Wilson, Cyrus J. Umrigar

Guillermo Palma

We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $ν$ and $η$ and the renormalization group flow of the probability density function of the magnetization. The results, compared to the standard Monte Carlo Renormalization Group proposed by Swendsen [1], are very accurate and the method works faster by a factor which grows monotonically with the lattice size. This allows to simulate larger lattices in reachable computational times.