at low temperatures*

We will present the results of the measurements of the heat capacity as a function of temperature on URu_2-xOs_xSi₂ alloys.  Our experimental results show that the critical temperature of the second-order phase transition increases while the value of the Sommerfeld coefficient in the ordered state decreases with 

an increase in osmium concentration. We also observe the increase in the values of the heat capacity at the critical temperature as well as a broadening

of the critical fluctuations region with an increase in x. We analyze the experimental data using the Haule-Kotliar model which, in particular, identifies the 

'hidden order' transition in the parent material URu₂Si₂ as a transition to a state with nonzero hexadecapole moment. We will demonstrate that our experimental 

results are consistent with the predictions of that model.