Ferromagnetism in perovskites RTiO 3 can be induced by a steric effect. How the subtle local structural change can induce 3D ferromagnetic coupling through Ti-O-Ti superexchange interactions remains controversial. The critical behavior study for the ferromagnetic phase has been made so far only on YTiO 3 since the magnetization measurements are plagued by the contribution from magnetic rare earth.Here we report critical exponents for most ferromagnetic members in the RTiO 3 family by measuring magnetocaloric effect and applying the corresponding scaling laws. Our results indicate that the ferromagnetic coupling in the RTiO 3 can be well-described by the 3D Heisenberg model. PACS numbers: 75.40. Cx, 75.47.Lx, 75.30.Sg 2 For a second-order ferromagnetic phase transition, the critical behavior near T c is characterized by a set of critical exponents 1 α, β, γ, and δassociated with, respectively, the specific heat C, the spontaneous magnetization M s (≡M H=0 ), the initial magnetic susceptibility χ 0 (≡ ∂M/∂H| H=0 ), and the critical isothermal M(H) T=Tc through the following equations:M s (T) ~ |T-T c | β (T < T c ),χ 0 (T) ~ |T-T c | -γ (T > T c ),M(H) ~ H 1/δ (T = T c ).These critical exponents are not independent and the number of independent variables is reduced to two by the following relations:Precise determination of these critical exponents can provide valuable information about a magnetic phase transition, e.g. the range and the dimensionality of the magnetic exchange interactions 2 .As shown in Table I, distinct values of the critical exponents corresponding to different models have been derived theoretically Parallel straight isothermal lines should be restored in the modified Arrott plot with the correct critical exponents.For most homogeneous ferromagnetic systems involving only one magnetization process, the above-mentioned Arrott-plot method is applicable. Otherwise, application of this method requires caution; interpretation of the obtained critical exponents must take into account the specific situation of the magnetic system. For example, in the RTiO 3 (R = Gd, …,Lu, and Y) perovskites, the critical behavior associated with the ferromagnetic ordering of the localized Ti 3+ S = ½ spin can be well understood in terms of the 3D Heisenberg model as shown in YTiO 3 . However, in these ferromagnetic RTiO 3 (R ≠ Y and Lu), the presence of large paramagnetic R 3+ moments near T c makes the Arrott-plot method invalid for the critical-behavior analysis. As shown in the present study on RTiO 3 , the Arrott-plot approach even leads to an opposite conclusion. Interestingly, during the course of our study on the magnetocaloric effect (MCE) of these ferromagnetic RTiO 3 11 , we found that the correct critical exponents can be deduced from the MCE scaling laws 12 .For a magnetic system with a second-order phase transition, Oesterreicher and Parker 14 have proposed a universal relation:where ΔS M PK is the peak value of the magnetic entropy change at different external magnetic fields H.Although subsequent experim...