We present the results of finite-temperature classical Monte Carlo simulations of a strongly spinorbit-coupled nearest-neighbor triangular-lattice model for the candidate U(1) quantum spin liquid YbMgGaO 4 at large system sizes. We find a single continuous finite-temperature stripe-ordering transition with slowly diverging heat capacity that completely breaks the sixfold ground-state degeneracy, despite the absence of a known conformal field theory describing such a transition. We also simulate the effect of random-bond disorder in the model, and find that even weak bond disorder destroys the transition by fragmenting the system into very large domains -possibly explaining the lack of observed ordering in the real material. The Imry-Ma argument only partially explains this fragility to disorder, and we extend the argument with a physical explanation for the preservation of our system's time-reversal symmetry even under a disorder model that preserves the same symmetry. arXiv:1801.06941v3 [cond-mat.str-el] 11 May 2018 -1.0 -0.5 0.5 1.0 J ±± J zz 0.25 0.5 0.75

Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study the mathematically tractable bipartite Sherrington-Kirkpatrick (SK) spin-glass model, which is formally similar to a restricted Boltzmann machine (RBM) neural network. The bipartite SK model has been previously studied assuming replica symmetry; here this assumption is relaxed and a replica symmetry breaking analysis is performed. The bipartite SK model is found to have many features in common with Parisi's solution of the original, unipartite SK model, including the existence of a multitude of pure states which are related in a hierarchical, ultrametric fashion. As an application of this analysis, the optimal cost for a graph partitioning problem is shown to be simply related to the ground state energy of the bipartite SK model. As a second application, empirical investigations reveal that the Gibbs sampled outputs of an RBM trained on the MNIST data set are more ultrametrically distributed than the input data themselves.

The electric or magnetic field of an ideal dipole is known to have a Dirac delta function at the origin. The usual textbook derivation of this delta function is rather ad hoc and cannot be used to calculate the delta-function structure for higher multipole moments. Moreover, a naive application of Gauss's law to the ideal dipole field appears to give an incorrect expression for the dipole's effective charge density. We derive a general result for the delta-function structure at the origin of an arbitrary ideal multipole field without using any advanced techniques from distribution theory. We find that the divergence of a singular vector field can contain a derivative of a Dirac delta function even if the field itself does not contain a delta function. We also argue that a physical interpretation of the delta function in the dipole field previously given in the literature is perhaps misleading and may require clarification.

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.

We use a semiclassical large-S expansion to study a plateau at 1/3 saturation in the magnetization curve of a frustrated ferrimagnet on a spatially anisotropic kagomé lattice. The spins have both ferromagnetic and antiferromagnetic nearest-neighbor Heisenberg couplings, and a frustrating nextnearest-neighbor coupling in one lattice direction. The magnetization plateau appears at the classical level for a certain range of couplings, and quantum fluctuations significantly broaden it at both ends. Near the region of the phase diagram where the classical plateau destabilizes, we find an exotic "chiral liquid" phase that preserves translational and U (1) spin symmetry, in which bound pairs of magnons with opposite spins are condensed. We show how this state is obtained naturally from a relativistic field theory formulation. We comment on the relevance of the model to the material Cu3V2O7(OH) 2 · 2H2O (volborthite).