Disorder- driven gradual transition of the continuous symmetry- breaking phase transition

Abstract

We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.