SOME REMARKS ON PHASE-TRANSITIONS GENERATED BY THE SUPERPOSITION OF MULTIFRACTALS

Emergence of novel second-order phase transitions by sums of multifrac tals was found by Radons and Stoop.(1,2) Using the same method as Rado ns and Stoop but different support, we have found that the second-orde r phase transitions are suppressed.(3) In this paper, we continue to e xtend the method to three multifractals, with the effect of the sums o f the three multifractals being the sums of two identical multifractal s and those of two different multifractals combined together. We have found that the resulted phase diagrams are more complicated, with seco nd-order phase transitions either partially or completely suppressed.