Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy

Details Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy

2003-09-25

arxiv.org/abs/cond-mat/0309573v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1088/0305-4470/36/43/014

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 $T_{\rm SG} \sim 0.19J$ 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 $\chi_{\rm SG}$ for $D = 0$ is obtained using almost the same transiton temperature of $T_{\rm SG} \sim 0.18J$. Hence we believe that the SG phase transition occurs in the Heisenberg SG model in $d = 3$.

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