Computing the roughening transition of Ising and solid-on-solid models by BCSOS model matching

TLDR: In this paper, the authors studied the roughening transition of the dual of the two-dimensional (2D) XY model, of the discrete Gaussian model, and of the absolute value solid-on-solid model and the interface in an Ising model on a threedimensional (3D) simple cubic lattice.

Abstract: We study the roughening transition of the dual of the two-dimensional (2D) XY model, of the discrete Gaussian model, of the absolute value solid-on-solid model and of the interface in an Ising model on a three-dimensional (3D) simple cubic lattice. The investigation relies on a renormalization group finite size scaling method that was proposed and successfully tested a few years ago. The basic idea is to match the renormalization group flow of the interface observables with that of the exactly solvable body-centred solid-on-solid (BCSOS) model. Our estimates for the critical couplings are , and for the XY model, the discrete Gaussian model and the absolute value solid-on-solid model, respectively. For the inverse roughening temperature of the Ising interface we find . To the best of our knowledge, these are the most precise estimates for these parameters published so far.