Studies of the specific heat Cp room temperature concentration dependences for the Bi1-xSbx (x = 0–0.12) solid solutions have shown that in the Cp(x) curves, three peaks of Cp are observed near x = 0.015, x = 0.037, and x = 0.07. These peaks are attributed to critical phenomena accompanying second-order concentration phase transitions (PT) from dilute to concentrated solid solutions, to a gapless state, and a semimetal–semiconductor transition, respectively. The numerical values for the critical exponents of the specific heat α for the Cp peaks near x = 0.015 and x = 0.037 have been determined within the framework of fluctuation theory for second-order phase transitions and percolation theory. It was shown that the α values (α = 0.11 ± 0.005) are the same within the margin of error for both peaks and correspond to the values theoretically calculated within the framework of scale-invariant theory for three–dimensional (3D) models and determined experimentally for different physical systems undergoing second-order phase transitions.