COMBINING MCRG AND FOURIER ACCELERATED LANGEVIN ALGORITHM

TL;DR

This paper demonstrates that combining Monte Carlo renormalization group with Fourier accelerated Langevin algorithms efficiently computes critical exponents in $$-dimensional $$-theory, matching other methods' accuracy.

Contribution

It introduces a novel combination of MCRG and Fourier accelerated Langevin algorithms for efficient critical exponent calculation.

Findings

Accurately computes critical exponents $ u$ and $$ in $$-dimensional $$-theory.

Achieves results comparable to other analytical methods.

Requires moderate computational resources.

Abstract

We study the implementation of Monte Carlo renormalization group (MCRG) in momentum space. This technique is most efficient when used in combination with a Fourier accelerated Langevin algorithm. As a benchmark we calculate the critical exponents $\nu$ and $\eta$ in the vicinity of both the gaussian and the Wilson fixed point in $\lambda \phi^4_3$. The results are very competitive with alternative analytical methods and require a moderate computational effort only.