Crossover behaviors in liquid region of vortex states above a critical point caused by point defects
Vortex states in high-$T_{\rm c}$ superconductors with point defects are studied by large-scale Monte Carlo simulations of the three-dimensional frustrated XY model. A critical point is observed on the first-order phase boundary between the vortex slush and vortex liquid phases. A step-like anomaly of the specific heat is detected in simulations of finite systems, similar to an experimental observation [F.~Bouquet {\it et al.}, Nature (London) {\bf 411}, 448 (2001)]. However, it diminishes with increasing system size, and the number and size distribution of thermally-excited vortex loops show continuous behaviors around this anomaly. Therefore, the present study suggests a crossover rather than a thermodynamic phase transition above the critical point.