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Register a new userGround state properties of two spin models with exactly known ground states on the square lattice
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We introduce a new two-dimensional model with diagonal four spin exchange and an exactly knownground-state. Using variational ansaetze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model. Both for this model and for the Shastry-Sutherland model we study periodic systems up to system size 6x6.
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We study the effect of perpendicular single-ion anisotropy, $-As_{text{z}}^2$, on the ground-state structure and finite-temperature properties of a two-dimensional magnetic nanodot in presence of a dipolar interaction of strength $D$. By a simulated annealing Monte Carlo method, we show that in the ground state a vortex core perpendicular to the nanodot plane emerges already in the range of moderate anisotropy values above a certain threshold level. In the giant-anisotropy regime the vortex structure is superseded by a stripe domain structure with stripes of alternate domains perpendicular to the surface of the sample. We have also observed an intermediate stage between the vortex and stripe structures, with satellite regions of tilted nonzero perpendicular magnetization around the core. At finite temperatures, at small $A$, we show by Monte Carlo simulations that there is a transition from the the in-plane vortex phase to the disordered phase characterized by a peak in the specific heat and the vanishing vortex order parameter. At stronger $A$, we observe a discontinuous transition with a large latent heat from the in-plane vortex phase to perpendicular stripe ordering phase before a total disordering at higher temperatures. In the regime of perpendicular stripe domains, namely with giant $A$, there is no phase transition at finite $T$: the stripe domains are progressively disordered with increasing $T$. Finite-size effects are shown and discussed.
The high-field ground state of the competing-spin-chain compound Cs2Cu2Mo3O12 with the ferromagnetic first-nearest-neighbor J1=-93 K and the antiferromagnetic second-nearest-neighbor J2 = +33 K was investigated by 133Cs-NMR. A divergence of T1-1 and a peak-splitting in spectra were observed at TN = 1.85 K, indicating the existence of a field-induced long range magnetic order. In the paramagnetic region above 4 K, T1-1 showed a power-law temperature dependence T2K-1. The exponent K was strongly field-dependent, suggesting the possibility of the spin-nematic Tomonaga Luttinger Liquid state.
We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special crossing symmetry. The crossing symmetry equates partition functions on different trivalent graphs, allowing a transformation to a graph where the partition function is easily computed. The simplest example is counting the number of nets without ends on the honeycomb lattice, including a weight per branching. Other examples include an Ising model on the Kagome lattice with three-spin interactions, dimers on any graph of corner-sharing triangles, and non-crossing loops on the honeycomb lattice, where multiple loops on each edge are allowed. We give several methods for obtaining models with this crossing symmetry, one utilizing discrete groups and another anyon fusion rules. We also present results indicating that for models which deviate slightly from having crossing symmetry, a real-space decimation (renormalization-group-like) procedure restores the crossing symmetry.
We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence bond solid ground states, b) critical and ordered Neel states on bipartite infinite Cayley trees and c) critical and ordered quantum vector spin glass states on random graphs of fixed connectivity. We argue, in consonance with a previous analysis, that all phases are characterized by gaps to local excitations. The spin glass states we report arise from random long ranged loops which frustrate Neel ordering despite the lack of randomness in the coupling strengths.
We consider the calculation of ground-state expectation values for the non-Hermitian Z(N) spin chain described by free parafermions. For N=2 the model reduces to the quantum Ising chain in a transverse field with open boundary conditions. Use is made of the Hellmann-Feynman theorem to obtain exact results for particular single site and nearest-neighbour ground-state expectation values for general N which are valid for sites deep inside the chain. These results are tested numerically for N=3, along with how they change as a function of distance from the boundary.
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