Abstract
We study phase transitions in classical spin ice at nonzero magnetization, by introducing a mean-field theory designed to capture the interplay between confinement and topological constraints. The method is applied to a model of spin ice in an applied magnetic field along the crystallographic direction and yields a phase diagram containing the Coulomb phase as well as a set of magnetization plateaux. We argue that the lobe structure of the phase diagram, strongly reminiscent of the Bose–Hubbard model, is generic to Coulomb spin liquids.
Highlights
Classical spin liquids [1], such as the Coulomb phase [2] in spin ice [3] and related systems, are examples of phases whose behavior is not captured by the standard Landau picture of broken symmetries [4]
We have shown that applying mean-field theory to the model defined by H in Eq (8) produces a phase diagram containing the Coulomb phase [2] as well as a fully-polarized paramagnet [9] and the Melko–den Hertog–Gingras (MDG) phase [22]
We have presented a mean-field theory designed to study confinement transitions, based on the analogy between the confinement criterion and long-range order in conventional ordering transitions
Summary
Classical spin liquids [1], such as the Coulomb phase [2] in spin ice [3] and related systems, are examples of phases whose behavior is not captured by the standard Landau picture of broken symmetries [4] Their two defining characteristics are fractionalization, the emergence of excitations not constructed from finite combinations of the elementary degrees of freedom, and topological order, the presence of structure that can only be discerned by observing the system globally [5]. Within the low-energy configuration space relevant at low temperatures, any local dynamics conserves the uniform magnetization [2] This fact is known to have interesting consequences for critical properties at certain confinement transitions, such as the Kasteleyn transition in an applied magnetic field [9, 10]
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