Abstract
Recently, a convergent series employing a non-Gaussian initial approximation was constructed and shown to be an effective computational tool for the finite size lattice models with a polynomial interaction. Here we show that the Borel summability is a sufficient condition for the correctness of the convergent series applied to infinite lattice models. We test the numerical workability of the convergent series method by examining one- and two-dimensional ϕ4-infinite lattice models. The comparison of the convergent series computations and the infinite lattice extrapolations of the Monte Carlo simulations reveals an agreement between two approaches.
Highlights
The development of effective computational methods for systems with a large number of degrees of freedom (d. o. f.) is the one of the main open problems in the modern theoretical physics
In this paper we have studied the applicability of the convergent series to the systems with an infinite amount of degrees of freedom
Considering φ4-model on the one and two-dimensional infinite lattices, we have provided a numerical evidence of the robustness of the CS method
Summary
The development of effective computational methods for systems with a large number of degrees of freedom (d. o. f.) is the one of the main open problems in the modern theoretical physics. The divergence of the standard perturbation theory (SPT) is caused by the incorrect interchange of the summation and integration due to the inaccurate account of large fluctuations of fields. In another words, the exponent of the polynomial interaction being expanded into the Taylor series, grows to fast at large fields with respect to the Gaussian initial approximation. Different aspects of the method, including the RG-analysis and strong coupling expansion, were developed in [13, 14, 15, 16] In all these earlier constructions the applicability of the dimensional regularization [17] to handle the limit of the infinite number of d. We consider the φ4-lattice model on the infinite lattice in one and two dimensions
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