Square-tiling model for the glass transition: transfer-matrix approach for the competing energy

Abstract

We introduce the correlation length for the square-tiling model for the glass transition through the transfer-matrix approach developed earlier [S. M. Bhattacharjee and E. Helfand, Phys. Rev. A 36, 3332 (1987)] for this model. We show that this transfer-matrix approach, in the limit when the competing internal energy reduces the model to the hard-square gas problem with nearest- and next-nearest-neighbor exclusion, is equivalent to the conventional row-to-row transfer matrix. Based on this, we propose that the transitions for other values of the coupling constant for the competing term are also nonuniversal, as is known for the hard-square gas problem.