The isotherms&sgr;T(H)and the high-field magnetization polytherms&sgr;H(T)of polycrystals of the dilute spin-glass systemLi0.5Fe2.5−xGaxO4are studied in the temperature range 4.2–380 K in fields up to 25 kOe. The nonmagneticGa3+ions in the crystals have concentrationsx=1.4and 1.6 in the vicinity of the multicritical pointx0=1.5on thex-Tphase diagram, near which all types of magnetic states have cluster-type spatially inhomogeneous structures. It is found that the dependences&sgr;H(T)obey Bloch’sT3/2law in the paramagnet temperature rangeT>Tf=18 K,x=1.6andT>TC=160 K,x=1.4forH⩾10 kOe.This is attributed to spin wave excitations in individual noninteracting clusters. TheT3/2law is violated atT<Tfforx=1.6,but is obeyed atT<TCforx=1.4.The clearly manifested phase transition at the Curie point in the form of a kink on the linear dependence&sgr;H(T3/2)suggests that the spin wave excitations are cooperative: their spectrum is formed atT⩽TCby the entire crystal, i.e., by the clusters and the matrix which is responsible for the long-range exchange coupling between clusters. At low temperatures, theT3/2law is violated atT∼50 K,where the sample withx=1.4previously displayed a first-order phase-transition. ©1998 American Institute of Physics.