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

摘要

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