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We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by the Bethe Ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.

The phase diagram of two coupled anisotropic spin-1/2 Heisenberg chains forming a ladder is studied via the finite-size machinery arising from conformal invariance. Our results show that this system has similar behaviour to the anisotropic spin-1 Heisenberg chain. Both models for low values of anisotropies have a massless phase of Gaussian type, governed by a c = 1 conformal field theory. The operator that destroys the massless phase in these models is the same as in the Gaussian picture. We also verify that the massive phase in the anisotropic Heisenberg ladder has the same type of nonlocal order as that in the spin-1 Heisenberg chain.

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S') SU(2) operator interacting with a XXZ like interaction (anisotropy $\Delta$). Our results indicate universal properties for all these chains. The whole phase, $1>\Delta>-1$, where the models change from ferromagnetic $( \Delta=1 )$ to ferrimagnetic $(\Delta=-1)$ behaviour is critical. Along this phase the critical fluctuations are ruled by a c=1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions., Comment: 21 pages, standard LaTex, to appear in J.Phys.A:Math.Gen

The phase diagram of the XXZ chain is calculated under the influence of homogeneous and staggered magnetic fields. The model has a rich phase structure with three types of phases. A fully ferromagnetic phase, an antiferromagnetic phase and a massless phase with partial ferromagnetic and antiferromagnetic order. This massless phase's critical fluctuations are governed by a conformal field theory with central charge c=1. When the sigma z-anisotropy Delta is zero the model is exactly integrable through a Jordan-Wigner fermionization and our results are analytic. For Delta not=0 our analysis is done numerically using lattice sizes up to M=20. Our results show that for -1

A study is made of the anisotropic biquadratic spin-1 Hamiltonian introduced by Batchelor et al. (1990). This model can be represented as a sum of operators satisfying a Temperley-Lieb algebra. Its critical behaviour is explored by using the relations between mass-gap amplitudes and critical exponents predicted by conformal invariance. The model, like in the XXZ chain, is found to exhibit a line of continuously varying exponents. By comparing its eigenspectrum with that of the XXZ Hamiltonian, several exact values are predicted.

We discuss the comments presented by Okamoto and Nomura about the phase diagram of the XXZ chain under the influence of an external staggered magnetic field, reported by Alcaraz and Malvezzi.