Critical Behavior in Random Magnetic Systems

Gabor Forgács, S. T. Chui, H. L. Frisch

Demetris Nicolaides

Magnetic systems containing randomly distributed fields with long-range correlations, decaying as a power law x−b exhibit new critical behavior at phase transitions in comparison to short-range random systems. When b<d+2, where d is the dimension of space, the critical behavior of the random system is the same as that of the pure one in an effective spatial dimension (b−2).

He-Ping Ying, Kenji Harada

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents straight theta,beta/nu, and z, for quenched disordered systems from the power-law behavior of the kth moments of magnetization.

Amnon Aharony A

Pasquale Calabrese, Andrea Pelissetto C, Ettore Vicari

We compute the crossover exponent $\ensuremath{\varphi}$ 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 ${\mathrm{Fe}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2}$ and ${\mathrm{Mn}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{F}}_{2},$ when applying an external magnetic field. Our result $\ensuremath{\varphi}=1.42(2)$ for the crossover exponent is in good agreement with the available experimental estimates.

Yoshitake Yamazaki