Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy

Abstract

We reexamine the spin glass (SG) phase transition of the $\pm J$ Heisenberg models with and without the random anisotropy $D$ in three dimensions ($d=3$) using complementary two methods, i.e., (i) the defect energy method and (ii) the Monte Carlo method. We reveal that the conventional defect energy method is not convincing and propose a new method which considers the stiffness of the lattice itself. Using the method, we show that the stiffness exponent $\theta$ has a positive value ($\theta >0$) even when $D=0$. Considering the stiffness at finite temperatures, we obtain the SG phase transition temperature of $T_{\mathrm{SG}}\sim 0.19J$ for $D=0$. On the other hand, a large scale MC simulation shows that, in contrary to the previous results, a scaling plot of the SG susceptibility ${\chi }_{\mathrm{SG}}$ for $D=0$ is obtained using almost the same transiton temperature of $T_{\mathrm{SG}}\sim 0.18J$. Hence we believe that the SG phase transition occurs in the Heisenberg SG model in $d=3$.

15 pages, 9 figures, to be published in J. Phys. A