Renormalized Field Theory of Quenched System under Gaussian Random Fields Conjugate to Anisotropic Spin Fields

Abstract

The effects of Gaussian random fields applied only to the m spin fields of the anisotropic (n+m)-vector model are studied in the quenched case via the renormalized rp' field theory by examining the stability of four fixed points and one fixed line in the large n and m limits. Regardless of the value of n/m, only a decoupled case is infrared stable, so that random fields prove to have no effects on the critical properties (e.g., critical indices) of the pure n spin fields. In such a decoupled case, as far as random fields are weak, longitudinal order corresponding to a random fixed point is observed remarkably. However, as the strength of random fields grows stronger, random fixed point moves to a Gaussian (trivial) fixed point and in consequence only transverse order gets conspicuous. The above. results are physically consistent with Aharony's arguments.