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The thermodynamic behavior of the spin $S=1/2$ antiferromagnetic two-legladder compound $(C_{5}H_{12}N)_{2} CuBr_{4}$ in a uniform magnetic field isstudied using numerical and analytical approaches. The entropy $S(H,T)$ andspecific heat $C(H,T)$ are calculated. The specific heat shows variousbehaviors in different regions of the magnetic field. The field-dependence ofthe specific heat is almost symmetric about the average of quantum criticalfields in complete agreement with experimental results. In addition, it isfound that during an adiabatic demagnetization process, temperature drops inthe vicinity of the field induced zero-temperature quantum phase transitions.

Thermodynamics of the spin-1/2 two-leg ladder compound $(C_{5}H_{12}N)_{2} CuBr_{4}$