Monte Carlo Calculations of the Specific Heat in Quantum Critical Metals

Quantum critical magnetic metals have unusual low temperature response such as an anomalous temperature dependence of the electronic specific heat (c$_{v}\sim $ T lnT). This dependence originates in the competition between ordering local magnetic moments and the conduction electrons shielding the moments. The Kondo Temperature, T$_{K}$ when moments become shielded depends on the inter-atomic distances. In most systems that have been investigated experimentally quantum criticality is obtained through lattice expansion by chemical substitution, one can expect a distribution of T$_{K}$ reflecting altered local inter-atomic distances. The random removal of these moments leads to the formation of magnetic clusters in quantum critical metals which has indeed been observed in quantum critical CeRu$_{0.5}$Fe$_{1.5}$Ge$_{2}$. We investigate the dependence of the specific heat through the formation through magnetic cluster formation. Once a cluster separates itself from the lattice, it should order and affect the specific heat.. Using a Monte Carlo simulation we calculate the changes in specific heat associated with cluster formation for various Kondo temperature distributions, and we compare our results to those measured in 122-systems like CeRu$_{0.5}$Fe$_{1.5}$Ge$_{2}$.