相关论文: Calculating critical temperature and critical expo…
The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric phi^4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques…
Self-similar sequence transformation is an original type of nonlinear sequence transformations allowing for defining effective limits of asymptotic sequences. The method of self-similar factor transformations is shown to be regular. This…
Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in powers of small variables to the…
A method is suggested for calculating the critical temperature in multicomponent field theory with weak interactions. The method is based on self-similar approximation theory allowing for the extrapolation of series in powers of…
We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by re-calculating the critical exponents of O(N)-symmetric $\vp^4$ theory. From only…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now…
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…
The problem is analyzed of extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar approximation theory. A new method is…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
Field theory at nonvanishing temperature beyond perturbation theory is discussed for the $N$-component $O(N)$-symmetric scalar theory. We compute the effective potential directly in three dimensions using an exact evolution equation for an…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi_{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{1 +…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several…
$\lambda\varphi^4$ theory at finite temperature suffers from infrared divergences near the temperature at which the symmetry is restored. These divergences are handled using renormalization group methods. Flow equations which use a fiducial…
The critical exponents and the critical amplitude ratio of the scalar model are determined using finite-temperature field theory with auxiliary mass. A new numerical method is developed to solve an evolution equation. The results are…
High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are…