Finite-size investigation of scaling corrections in the square-lattice three-state Potts antiferromagnet square-lattice three-state Potts antiferromagnet

Abstract

We investigate the finite-temperature corrections to scaling in the three-state square-lattice Potts antiferromagnet, close to the critical point at T=0. Numerical diagonalization of the transfer matrix on semi-infinite strips of width $L$ sites, $4 \leq L \leq 14$, yields finite-size estimates of the corresponding scaled gaps, which are extrapolated to $L\to\infty$. Owing to the characteristics of the quantities under study, we argue that the natural variable to consider is $x \equiv L e^{-2\beta}For the extrapolated scaled gaps we show that square-root corrections, in the variable $x$, are present, and provide estimates for the numerical values of the amplitudes of the first-- and second--order correction terms, for both the first and second scaled gaps. We also calculate the third scaled gap of the transfer matrix spectrum at T=0, and find an extrapolated value of the decay-of-correlations exponent, $\eta_3=2.00(1)$. This is at odds with earlier predictions, to the effect that the third relevant operator in the problem would give $\eta_{{\bf P}_{\rm stagg}}=3$, corresponding to the staggered polarization.