Using the recently developed transfer-matrix renormalization group method, we have studied the thermodynamic properties of two-leg antiferromagnetic ladders in a magnetic field. Based on different magnetization behaviors, we found a disordered spin liquid, the Luttinger liquid, spin-polarized phases, and a classical regime. Our calculations in the Luttinger liquid regime suggest that both the divergence of the NMR relaxation rate and the anomalous specific heat behavior observed on ${\mathrm{Cu}}_2({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2{)}_2{\mathrm{Cl}}_4$ are due to a quasi-one-dimensional effect rather than three-dimensional ordering.

• Received 1 July 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.5399