Confinement of monopoles and scaling theory near unconventional critical points

Abstract

Conventional ordering transitions, described by the Landau paradigm, are characterized by the symmetries broken at the critical point. Within the constrained manifold occurring at low temperatures in certain frustrated systems, unconventional transitions are possible that defy this type of description. While the critical point exists only in the limit where defects in the constraint are vanishingly rare, unconventional criticality can be observed throughout a broad region of the phase diagram. This work presents a formalism for incorporating the effects of such defects within the framework of scaling theory and the renormalization group, leading to universal results for the critical behavior. The theory is applied to two transitions occurring within a model of spin ice, and the results are confirmed using Monte Carlo simulations. Relevance to experiments, particularly in the spin-ice compounds, is discussed, along with implications for simulations of related transitions, such as the cubic dimer model and the O(3) sigma model with "hedgehog" suppression.

18 pages, 11 figures

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Cited by in corpus (13)

• Scaling dimensions of higher-charge monopoles at deconfined critical points
• Critical behavior in the cubic dimer model at nonzero monomer density
• Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet
• Ferromagnetic Coulomb phase in classical spin ice
• Half-Magnetization Plateau of a Dipolar Spin Ice in a [100] Field
• A cluster algorithm for Monte Carlo simulations of spin ice
• Tunable critical correlations in kagome ice
• Synchronization transition in the double dimer model on the cubic lattice
• Derivation of field theory for the classical dimer model using bosonization
• Crossover from string to cluster dynamics following a field quench in spin ice
• Dynamic scaling theory for a field quench near the Kasteleyn transition in spin ice
• Mean-field theory for confinement transitions and magnetization plateaux in spin ice
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench