Stability of commensurate phases of a planar model with competing interactions

Abstract

We study a one-dimensional planar model with competing interactions at zero temperature in the limit of low and high external magnetic fields. The stability of commensurate phases with wave number q 0 ϭ2( P/Q), where P/Q is an irreducible fraction, is discussed in the continuum approximation. We show that for small fields H→0ϩ, the helical phase with period QϾ4 has a width proportional to H Q/2 . Similarly, for high fields H→H c Ϫ, where H c is the critical field for the parafan transition, the fan phase with period Qу4 has a width proportional to ͉HϪH c ͉ (QϪ2)/4 if Q is an even number and ͉HϪH c ͉ (QϪ1)/2 if Q is an odd number.