Monopole-like configurations in the O(3) spin model at the upper critical dimension

TL;DR

This study uses high-precision Monte Carlo simulations to explore monopole-like topological excitations in the four-dimensional O(3) spin model, revealing agreement with quantum field theory predictions and implications for physics beyond classical constraints.

Contribution

First detailed numerical analysis of monopole-like configurations in the 4D O(3) model, linking lattice results with quantum field theory predictions.

Findings

Monopole-like excitations observed near the critical point.

Quantitative agreement with analytic quantum-field-theoretical predictions.

Implications for violation of Derrick's theorem at the quantum level.

Abstract

We present a high-precision Monte Carlo study of the O(3) spin theory on the lattice in four dimensions. This model exhibits interesting dynamical features, in particular in the broken-symmetry phase, where suitable boundary conditions can be used to enforce monopole-like topological excitations. We investigate the Euclidean time propagation and the features of these excitations close to the critical point, where our numerical results show an excellent quantitative agreement with analytic predictions derived from purely quantum-field-theoretical tools by G. Delfino. We conclude by commenting on the implications of our findings for a conjectured violation of Derrick's theorem at the quantum level and on the consequences in various areas of physics, ranging from condensed matter to astro-particle physics.