Studies of critical phenomena and phase transitions in large lattices with Monte-Carlo based non-perturbative approaches

TL;DR

This paper investigates critical phenomena and phase transitions in large lattice spin models using Monte Carlo simulations, providing evidence supporting non-perturbative theories and challenging traditional perturbative predictions.

Contribution

It offers large-scale Monte Carlo simulation results that support the GFD non-perturbative theory and suggests revised critical exponents for the 3D Ising model.

Findings

Monte Carlo results support GFD theory's nontrivial exponents.

Finite-size scaling indicates eta may be larger than perturbative RG predictions.

Data fits well with GFD exponents eta=1/8 and nu=2/3.

Abstract

Critical phenomena and Goldstone mode effects in spin models with O(n) rotational symmetry are considered. Starting with the Goldstone mode singularities in the XY and O(4) models, we briefly review different theoretical concepts as well as state-of-the art Monte Carlo simulation results. They support recent results of the GFD (grouping of Feynman diagrams) theory, stating that these singularities are described by certain nontrivial exponents, which differ from those predicted earlier by perturbative treatments. Furthermore, we present the recent Monte Carlo simulation results of the three-dimensional Ising model for very large lattices with linear sizes up to L=1536. These results are obtained, using a parallel OpenMP implementation of the Wolff single cluster algorithm. The finite-size scaling analysis of the critical exponent eta, assuming the usually accepted correction-to-scaling exponent omega=0.8, shows that eta is likely to be somewhat larger than the value 0.0335 +/- 0.0025 of the perturbative renormalization group (RG) theory. Moreover, we have found that the actual data can be well described by different critical exponents: eta=omega=1/8 and nu=2/3, found within the GFD theory.