By means of the generalized static replica symmetric spin glass theory, a quantum Heisenberg S=1/2 spin glass model with the infinite-ranged random Dzyaloshinskii-Moriya (DM) interaction and ferromagnetic coupling is investigated. The dependence of entropy, specific heat, susceptibility and the corresponding order parameters on temperature is studied numerically for different ferromagnetic interactions and fixed anisotropy. Two spin glass phases has been found including transverse and mixed spin glass phases. It has been shown that the local susceptibility exhibits double-cusp features for different ferromagnetic coupling (J(0)). Phase transition poins are found in the specific heat-temperature plane at various ferromagnetic coupling values. Additionally, the dependence of the spontaneous moment on temperature is calculated.
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