Specific-heat anomaly in frustrated magnets with vacancy defects

Motivated by frustrated magnets and spin-liquid-candidate materials, we study the thermodynamics of a 2D geometrically frustrated magnet with vacancy defects. The presence of vacancies imposes significant constraints on the bulk spins, which freeze some of the degrees of freedom in the system at low temperatures. With increasing temperature, these constraints get relaxed, resulting in an increase in the system's entropy. This leads to the emergence of a peak in the heat capacity $C(T)$ of the magnet at a temperature $T_\text{imp}$ determined by the concentration of the vacancy defects. The entropy associated with this peak comes from the lowest-energy degrees of freedom in the material. To illustrate the emergence of such an anomaly, we compute analytically the heat capacity of the antiferromagnetic (AFM) Ising model on the triangular lattice with vacancy defects. The presence of the vacancy leads to a peak in $C(T)$ at the temperature $T_\text{imp}=-4J/\ln n_\text{imp}$, where $J$ is the AFM coupling between the spins and $n_\text{imp}$ is the fraction of the missing sites.