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, $4\le L\le 14$, 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 $x\equiv L{e}^{-2\beta }Fortheextrapolatedscaledgapsweshowthatsquare-rootcorrections,inthevariable$x$,arepresent,andprovideestimatesforthenumericalvaluesoftheamplitudesofthefirst--andsecond--ordercorrectionterms,forboththefirstandsecondscaledgaps.WealsocalculatethethirdscaledgapofthetransfermatrixspectrumatT=0,andfindanextrapolatedvalueofthedecay-of-correlationsexponent,$η_3=2.00(1)$.Thisisatoddswithearlierpredictions,totheeffectthatthethirdrelevantoperatorintheproblemwouldgive$η_{{\bf P}_{\rm stagg}}=3$, corresponding to the staggered polarization.

RevTex4, 5 pages, 2 .eps figures included

References in corpus (1)

• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice

Cited by in corpus (1)

• Phase Diagram of the Square-Lattice Three-State Potts Antiferromagnet with Staggered Polarization Field