Abstract
We analyze the zero-temperature phase diagram of two kinds of one-dimensional quantum-spin models in a transverse magnetic field. The first kind has uniform nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic couplings. A spin-wave analysis indicates the presence of several (possibly an infinite number of) commensurate modulated phases in the phase diagram. The three most prominent phases are paramagnetic, ferromagnetic, and a q=(1/4 phase of period four. The second kind of model is a spin-glass with only nearest-neighbor ferromagnetic interactions whose strengths are random and are characterized by a probability function. A classical large-S analysis shows the existence of a Griffiths phase lying in between a low-magnetic-field ferromagnetic phase and a high-magnetic-field paramagnetic phase. We present two order parameters that can together distinguish between the three phases.
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