Untitled

Abstract

Within the massive field theoretical renormalization group approach the expressions for the β-and γ-functions of the anisotropic mn-vector model are obtained for general space dimension d in three-loop approximation. Resumming corresponding asymptotic series, critical exponents for the case of the weakly diluted quenched Ising model (m = 1, n = 0), as well as estimates for the marginal order parameter component number m c of the weakly diluted quenched m-vector model are calculated as functions of d in the region 2 ≤ d < 4. Conclusions concerning the effectiveness of different resummation techniques are drawn.

Continued functions and perturbation series: Simple tools for convergence of diverging series in $O(n)$-symmetric $\phi^4$ field theory at weak coupling limit

“…3.2. Critical exponents for non-integer dimensions Critical exponents for non-integer dimensions have also been obtained by resummation methods [37,38,39,40], high-temperature expansion [41] and finite-size-scaling method [42]. To illustrate this simple method provides reasonable values in different dimensions we compare our results of ν and γ with n = 1 for 1 < d ≤ 2 in table 7.…”

Three-dimensional Ising model confined in low-porosity aerogels: A Monte Carlo study

“…After these experimental results one may take noncorrelated SRC instead of LRC disorder within aerogels to be the relevant one for the critical behavior of the 3DIS model in aerogel pores. 8 Renormalization group ͑RG͒ calculations for the 3DIS with weak amounts of disorder show that a new universality class appears, different from that of the pure 3DIS, 12,13,[24][25][26][27][28] and consistent with Harris criterion. Since Landau, 29 using MC simulations, concluded that the exponents for the 3DIS model with random impurities differ from those of the pure system, different works stated that the exponents depend on the concentration of impurities, until 1990, when Heuer 30,31 began to clarify that differences with RG calculations are due to the fact that exponents obtained from simulations were basically effective ones, and not the asymptotic ones.…”

“…Most numerical and theoretical works address the random-diluted 3DIS ͑RDIS͒ model-i.e., the Ising model in the presence noncorrelated distributions of impurities. [11][12][13][14][15] Apart, concerning disordered LRC structures, Ballesteros and Parisi 16 simulated the 3DIS model, with dislocations represented by lines of impurities generated at random. Correlations for this type of disorder decay with an exponent a = 2.…”

DNA thermal denaturation by polymer field theory approach: effects of the environment

“…The derivation given below is based on these double ε, δ expansions. In particular, it has been shown that for certain 2See also [56][57][58], where the relation of fractal dimension to the analytically continued non-integer dimension is discussed in more details. region of parameters ε/2 < δ < ε, the scaling properties of a single flexible polymer chain in porous environment with a long-range correlated structure are governed by a new, 'long-range' fixed point L.…”