Boundary critical behavior of the three-dimensional Heisenberg universality class

TL;DR

This paper investigates the boundary critical phenomena of the 3D Heisenberg universality class using high-precision Monte Carlo simulations, revealing a special phase transition with unique exponents and an extraordinary phase with logarithmic correlations.

Contribution

It provides the first high-precision numerical evidence for a boundary phase transition and an extraordinary phase in the 3D Heisenberg model, clarifying previous theoretical puzzles.

Findings

Existence of a special boundary phase transition with unusual exponents

Identification of an extraordinary phase with logarithmic decay of correlations

Resolution of previous puzzles in boundary critical behavior of quantum spin models

Abstract

We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk scaling corrections are suppressed, we prove the existence of a special phase transition, with unusual exponents, and of an extraordinary phase with logarithmically decaying correlations. These findings contrast with na\"ive arguments on the bulk-surface phase diagram, and allow us to explain some recent puzzling results on the boundary critical behavior of quantum spin models.