Low-temperature renormalization group for the Lifshitz point

The momentum-shell technique is employed to derive the recursion relations for the Lifshitz point above the lower critical dimensionality. For the uniaxial point (m=1) the expansion is made in ε=d-2.5 and the critical exponents are calculated. The results are λt=ν4-1=2ε, η2=ε(n-2), η4=2ε(n-2), βk=12+3ε4(n-2), where n is the number of components of the spin. The critical behavior in the presence of long-range power-law interactions is also studied. © 1978 The American Physical Society.