scholarly journals WEAK QUENCHED DISORDER AND CRITICALITY: RESUMMATION OF ASYMPTOTIC(?) SERIES

2002 ◽  
Vol 16 (27) ◽  
pp. 4027-4079 ◽  
Author(s):  
YU. HOLOVATCH ◽  
V. BLAVATS'KA ◽  
M. DUDKA ◽  
C. VON FERBER ◽  
R. FOLK ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Critical Behavior ◽  
Asymptotic Series ◽  
Analytical Description ◽  
Quenched Disorder ◽  
Site Disorder ◽  
Disordered Models ◽  
Random Site ◽  
Theoretical Results ◽  
Theory Series

In this review paper, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of the available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of this review is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.

scholarly journals Critical behavior of the 2d scalar theory: resumming the N8LO perturbative mass gap

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Gustavo O. Heymans ◽  
Marcus Benghi Pinto
Keyword(s):  
Perturbation Theory ◽  
Critical Behavior ◽  
State Of The Art ◽  
Critical Coupling ◽  
Scalar Theory ◽  
Perturbative Series ◽  
Supercritical Region ◽  
Mass Gap ◽  
Perturbative Result ◽  
Symmetric Phase

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

Calculation of vibrational HDO energy levels: Analysis of perturbation theory series

2013 ◽  
Vol 114 (3) ◽  
pp. 359-367 ◽  
Author(s):  
A. D. Bykov ◽  
K. V. Kalinin ◽  
A. N. Duchko
Keyword(s):  
Perturbation Theory ◽  
Energy Levels ◽  
Theory Series

Non-Equilibrium Critical Dynamics of Ferromagnets with Long Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 31-34
Author(s):  
Dmitry N. Kulikov ◽  
Pavel V. Prudnikov
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Behavior ◽  
Disordered Systems ◽  
Asymptotic Series ◽  
Three Dimensional ◽  
Time Regime ◽  
Short Time ◽  
Short Time Evolution ◽  
Non Equilibrium

The simultaneous effect of non-equilibrium initial states and correlation betweendefects of the structure on the evolution of anisotropic disordered systems at the critical pointwas analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dy-namical critical exponent of the short-time evolution was calculated in the two-loop approxima-tion without the use of the "-expansion. The values of the dynamical critical exponent obtainedby using various methods for summing asymptotic series were compared with the results ofthe computer simulation of the non-equilibrium critical behavior of the three-dimensional dis-ordered Ising model in the short-time regime.

The calculation of higher-order energies in the many-body perturbation theory series

1985 ◽  
Vol 113 (1) ◽  
pp. 8-12 ◽  
Author(s):  
P.J. Knowles ◽  
K. Somasundram ◽  
N.C. Handy ◽  
K. Hirao
Keyword(s):  
Perturbation Theory ◽  
Higher Order ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
The Many ◽  
Theory Series
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