Critical exponents in two dimensions and pseudo-ε expansion.
The critical behavior of two-dimensional n-vector λϕ4 field model is studied within the framework of pseudo-ε expansion approach. Pseudo-ε expansions for Wilson fixed-point location g* and critical exponents originating from five-loop two-dimensional renormalization-group series are derived. Numerical estimates obtained within Padé and Padé-Borel resummation procedures as well as by direct summation are presented for n=1, n=0, and n=-1, i.e., for the models which are exactly solvable. The pseudo-ε expansions for g*, critical exponents γ, and ν have small lower-order coefficients and slow increasing higher-order ones. As a result, direct summation of these series with optimal cutoff provides numerical estimates that are no worse than those given by the resummation approaches mentioned. This enables one to consider the pseudo-ε expansion technique itself as some specific resummation method.
Department of Quantum Mechanics, Saint Petersburg State University, Ulyanovskaya 1, Petergof, Saint Petersburg, 198504, Russia.
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Nikitina
Department of Quantum Mechanics, Saint Petersburg State University, Ulyanovskaya 1, Petergof, Saint Petersburg, 198504, Russia.
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Sokolov