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We present measurements of the magnetic entropy landscape and Grüneisen parameter of the Cu2+ complex (C5 H12 N)2 CuCl4 in a magnetic field. Our thermodynamic measurements are in very good agreement with a theoretical description by a S = 1/2 Heisenberg ladder model. Due to its excellent experimental access, the compound crosses two quantum critical points in the applied range of the magnetic field, first from a gapped unpolarized state to a critical phase and then to a gapped fully polarized state. This behavior is reflected directly in the magnetic entropy map. Due to the remarkable properties of the magnetic Gru ̈neisen parameter, we are able to discuss the validity of critical behavior with respect to temperature and magnetic field for this model quasi-one-dimensional system.

Motivated by recent experiments on Ni(C_{2}H_{8}N_{2})_{2}Ni(CN)_{4} (commonly known as NENC), we study the electron spin resonance in the critical high-field phase of the antiferromagnetic S=1 chain with strong planar anisotropy and show that the ESR spectra exhibit several peculiarities in the critical phase. Possible relevance of those results for other gapped spin systems is discussed., Comment: 8 revtex pages, 1 eps figure included

We calculate the quantum phase diagram of the {\it XXZ} chain with nearest-neighbor (NN) $J_{1}$ and next-NN exchange $J_{2}$ with anisotropies $\Delta_{1}$ and $\Delta_{2}$ respectively. In particular we consider the case $\Delta_{1}=-\Delta_{2}$ to interpolate between the {\it XX} chain ($% \Delta_{i}=0$) and the isotropic model with ferromagnetic $J_{2}$. For $% \Delta_{1}, Comment: 10 pages, 4 psfigures

The one-dimensional spin-$S {J}_{1}\ensuremath{-}{J}_{2}\mathrm{XY}$ model is studied within the bosonization approach. Around the two limits ${(J}_{2}{/J}_{1}\ensuremath{\ll}1, {J}_{2}{/J}_{1}\ensuremath{\gg}1)$ where a field theoretical analysis can be derived, we discuss the phases as well as the different phase transitions that occur in the model. In particular, it is found that the chiral critical spin nematic phase, discovered by Nersesyan et al. [Phys. Rev. Lett. 81, 910 (1998)] for $S=1/2,$ exists in the general spin-$S$ case. The nature of the effective-field theory that describes the transition between this chiral critical phase and a chiral gapped phase is also determined.