Crossover from random-exchange to random-field critical behavior in Ising models

Abstract

We compute the crossover exponent $\varphi$ describing the crossover from the random-exchange to the random-field critical behavior in Ising systems. For this purpose, we consider the field-theoretical approach based on the replica method, and perform a six-loop calculation in the framework of a fixed-dimension expansion. The crossover from random-exchange to random-field critical behavior has been observed in dilute anisotropic antiferromagnets, such as Fe${}_x$Zn${}_{1-x}$F${}_2$ and Mn${}_x$Zn${}_{1-x}$F${}_2$, when applying an external magnetic field. Our result $\varphi =1.42(2)$ for the crossover exponent is in good agreement with the available experimental estimates.

5 pages