Low Temperature Results for the Heisenberg XXZ and XY Models

摘要: This thesis contains two results for the low temperature behavior of quantum spin systems. First, we present a lower bound spin-1 XXZ chain in finite volumes in terms gap two-site Hamiltonian. The estimate is derived by method developed Nachtergaele (cond-mat/9410110) called Martingale Method. Our relies on an assumption which have, as yet, been unable to verify analytically all cases. We numerical evidence that strongly indicates our valid. second result proof spin-1/2, d-dimensional XY model presence an external magnetic field does not undergo phase transition at temperature, provided the strength great enough. Using contour expansion inspired Kennedy, we show weights contours satisfy condition Kotecky and Preiss allows us express free energy system cluster expansion. As part setup give simple all-spin-up state unique ground when has least 2d.