Experimental validation of nonextensive statistical field theory: Applications to manganites

Is γ-generalized statistical field theory complete?

“…Although γ KLS -SFT can explain the results for the Tables I-II, it does not explain the results of Table IV for some materiais, being explained only for NSFT (see Table IV) of Ref. [21]. Then, γ KLS -SFT must be discarded as one trying to generalize statistical mechanics.…”

“…Recently, a field-theoretic renormalization group method for describing the unconventional critical behavior of some real imperfect systems known as manganites [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] was proposed [21]. These systems are complex and present a large number of strong interacting particles, defects, impurities, inhomogeneities, nonlinearities, competition etc.…”

“…Such systems can not be understood by employing standard Gibbs-Boltzmann statistical field theory (SFT) formulated by Kenneth Wilson [22]. Rather, we have to employ some generalized version of Wilson field-theoretic renormalization group, namely nonextensive statistical field theory (NSFT) [21]. As it is known, there are many attempts of generalizing Gibbs-Boltzmann statistical mechanics [23][24][25][26][27].…”

“…Then it has to be discarded as one candidate to generalize statistical mechanics. In fact, recently it was shown that it was the case for Kaniadakis attempt for generalizing statistical mechanics [28], i. e., this statistics, namely Kaniadakis statistics [24] does not describe the set of unconventional critical exponents values for some manganites as NSFT does [21].…”

“…The aim of this Letter is to search if there are some field-theoretic renormalization group generalizations sat- * prscarvalho@ufpi.edu.br isfying all the requirements aforementioned other than NSFT (parameterized by the parameter q encoding some effective interaction [21]). For that, we employ the γ KLSgeneralized statistics proposed in Ref.…”