Extended scaling relations for the chiral and cubic crossover exponents

The critical dimensions xCH(q) of the chiral and xCB(q) of the cubic operator in the two-dimensional q-state Potts model satisfy the extended scaling relations xCH=(n2-y2)/(4x)+x and xCB=(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 xCH is relevant, but takes the special value xT+1=9/5. The crossover exponent at the percolation point in the bond-diluted random Ising model, determined by xCB at q=1, is equal to one. Along the Baxter line in the Ashkin-Teller, eight-vertex and ANNNI model xCH=xT/4+1/xT.