On the evaluation of the specific heat and general off-diagonal n-point   correlation functions within the loop algorithm
  We present an efficient way to compute diagonal and off-diagonal n-point correlation functions for quantum spin-systems within the loop algorithm. We show that the general rules for the evaluation of these correlation functions take an especially simple form within the framework of directed loops. These rules state that contributing loops have to close coherently. As an application we evaluate the specific heat for the case of spin chains and ladders. 
J. V. Alvarez and Claudius Gros