Topological excitations in statistical field theory at the upper critical dimension

TL;DR

This study uses high-precision Monte Carlo simulations to demonstrate the existence of topological monopole-like excitations in the four-dimensional classical Heisenberg model, confirming analytical predictions and suggesting experimental relevance.

Contribution

It provides the first numerical evidence of topological excitations in the 4D classical Heisenberg model, aligning with quantum field theory predictions.

Findings

Topological monopole-like excitations exist in the 4D classical Heisenberg model.

Properties of these excitations match analytical predictions.

Potential implications for condensed-matter experiments.

Abstract

We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions, showing that in the broken-symmetry phase it supports topological, monopole-like excitations, whose properties confirm previous analytical predictions derived in quantum field theory. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.