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

Calabrese, Pasquale and Pelissetto, Andrea and Vicari, Ettore (2003) Crossover from random-exchange to random-field critical behavior in Ising models. Physical review. B, Condensed matter and materials physics, 68 . 092409. ISSN 1550-235X

Abstract

We compute the crossover exponent $\phi$ 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 $\phi=1.42(2)$ for the crossover exponent is in good agreement with the available experimental estimates.

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