Optimized Factor Approximants and Critical Index

Based on expansions with only two coefficients and known critical points, we consider a minimal model of phenomena. The method analysis is both based inspired the symmetry properties functional self-similarity relation between consecutive approximations. Factor approximants are applied together various natural optimization conditions non-perturbative nature. role control parameter played by index itself. derivative condition imposed amplitude appears to bring most reasonable, uniquely defined results. difference also amplitudes produces upper lower bound index. While one bounds close result from condition, second determined non-optimized factor approximant. One would expect that for work well, should be not too wide. In this sense technique presented above self-consistent, since it automatically supplies solution bounds. case effective viscosity passive suspensions could found wide make any either solutions. Other approximants, lead better estimates viscosity. equating explicit expressions following different definitions index, while introduced as trial third-order coefficient in expansion.