Heat capacity and magnetization of CoNb$_2$O$_6$ near quantum critical point*

CoNb$_2$O$_6$ is a quasi-1D quantum magnet in which magnetic Co$^{2+}$ ions are ferromagnetically arranged into nearly isolated chains along the c axis with the magnetic moment confined in the ac-plane. By applying transverse magnetic field along b-axis, quantum phase transition from magnetically ordered phase to paramagnetic phase occurs. Evidence for emergent E$_8$ symmetry was recently obtained by neutron scattering near the quantum critical point (QCP) in an applied transverse magnetic field of 5.5 T We will report on experiments to investigate the behavior of the heat capacity and torque magnetization in the vicinity of the QCP and discuss their implications.