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