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 coupl
ing is investigated. The dependence of entropy, specific heat, suscept
ibility and the corresponding order parameters on temperature is studi
ed numerically for different ferromagnetic interactions and fixed anis
otropy. Two spin glass phases has been found including transverse and
mixed spin glass phases. It has been shown that the local susceptibili
ty exhibits double-cusp features for different ferromagnetic coupling
(J(0)). Phase transition poins are found in the specific heat-temperat
ure plane at various ferromagnetic coupling values. Additionally, the
dependence of the spontaneous moment on temperature is calculated.