In this paper we study the critical behavior of an N -component φ 4 -model in hyperbolic space, which serves as a model of uniform frustration. We find that this model exhibits a second-order phase transition with an unusual magnetization texture that results from the lack of global parallelism in hyperbolic space. Angular defects occur on length scales comparable to the radius of curvature. This phase transition is governed by a new strong curvature fixed point that obeys scaling below the upper critical dimension duc = 4. The exponents of this fixed point are given by the leading order terms of the 1/N expansion. In distinction to flat space no order 1/N corrections occur. We conclude that the description of many-particle systems in hyperbolic space is a promising avenue to investigate uniform frustration and non-trivial critical behavior within one theoretical approach. arXiv:1507.02909v1 [cond-mat.stat-mech] 10 Jul 2015
In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multi-spin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling, we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type and at lower temperatures, we find long-range Z6 order.
Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-d and O-p orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the p-orbitals inevitably generate a biquadratic coupling between the spins of the d-orbitals. The key point revealed by our classical Monte Carlo simulations and large-N calculations is that the biquadratic term favors local stripelike magnetic fluctuations, which result in an enhanced nematic susceptibility that onsets at a temperature scale determined by the effective Heisenberg exchange J. We discuss the impact of this type of nematic order on the magnetic spectrum and outline possible implications on our understanding of nematicity in the cuprates.Here, t ij denotes the hole hopping parameters and J the AFM exchange coupling. The operator S i = 1 2 αβd † iα σ αβdiβ describes the d-orbital spin and n i = αd † iαd iα the corresponding charge. The strong local Coulomb interaction is incorporated in terms of the hole creation operatord † iα = (1 − n iᾱ ) d † iα , reflecting the fact that double occupancy of the sites is not allowed near the Mott insulating state.As we demonstrate below via a strong coupling expansion of the Emery model, the inclusion of the p-orbitals leads to an important additional term in the t − J Hamiltonian. While the two terms in Eq. (1) remain the same, albeit with a different microscopic expression for J, non-critical quadrupolar fluctuations of the p-orbitals, enhanced by the repulsion between p-orbitals, generate a positive biquadratic coupling K > 0 between the dorbital spins:resulting in an effective t−J −K Hamiltonian, H t−J−K = H t−J + H K .arXiv:1703.02210v2 [cond-mat.str-el]
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