Extended scaling relations for the chiral and cubic crossover exponents

Abstract

The critical dimensions x_CH(q) of the chiral and x_CB(q) of the cubic operator in the two-dimensional q-state Potts model satisfy the extended scaling relations x_CH=(n²-y²)/(4x)+x and x_CB=(m²-y²)/(4x)+x with x+y=2, 2 cos( pi y/2)= square root q, n an odd and m an even integer; n=1 and m=0 give the leading exponents. At q=3 x_CH is relevant, but takes the special value x_T+1=9/5. The crossover exponent at the percolation point in the bond-diluted random Ising model, determined by x_CB at q=1, is equal to one. Along the Baxter line in the Ashkin-Teller, eight-vertex and ANNNI model x_CH=x_T/4+1/x_T.