M Hasenbusch and K Pinn 1997 J. Phys. A: Math. Gen. 30 63 doi:10.1088/0305-4470/30/1/006
Computing the roughening transition of Ising and solid-on-solid models by BCSOS model matching
M Hasenbusch
and K Pinn
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.
- PACS
-
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
-
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B28 Renormalization group methods (See also 81T17)
82B26 Phase transitions (general)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
- Subjects
- Dates
-
Issue 1 (7 January 1997)
Received 10 May 1996, in final form 18 September 1996
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Computing the roughening transition of Ising and solid-on-solid models by BCSOS model matching
M Hasenbusch and K Pinn 1997 J. Phys. A: Math. Gen. 30 63
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