Topological excitations in statistical field theory at the upper critical dimension

Abstract

We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.

Spontaneous symmetry breaking via inhomogeneities and the differential surface tension

“…We note that similar inhomogeneities can also be discussed employing boundary conditions instead of constraints, see e.g. [23,24].…”

Mass of quantum topological excitations and order parameter finite size dependence

“…It follows that, if the topological particle has an infinite mass, the order parameter becomes R-independent in the large R limit we consider. The absence of an appreciable R-dependence of the one-point functions is the key difference observed in the numerical simulations of [8,9] for n = 3 with respect to those of [6] for n = 2. We now see that this difference is explained by the theory and indicates that the topological mass m τ is infinite for n = 3, i.e.…”

“…It is interesting to extend the analyis to the energy density field ε ∝ s 2 , which was also simulated in [6,8]. Recalling ( 9) and ( 14), the result of ( 6) for this field will take the form…”

“…More recently, the program of [6] has been carried through in [8,9] for the O(3) scalar theory in d = 4. Intriguingly, the numerical simulations showed a scaling dependence on the parameters-the finite size R and the deviation from criticality-markedly different from that observed in [6].…”

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

“…In this contribution we present our latest work [1], regarding the study of the classical Heisenberg model at the upper critical dimension. This model experiences a phase transition at the critical temperature, allowing us to distinguish two phases in which the overall symmetry of the system is either spontaneously broken or restored [2].…”