Configurational temperature: Verification of Monte Carlo simulations

A new diagnostic that is useful for checking the algorithmic correctness of Monte Carlo computer programs is presented. The check is made by comparing the Boltzmann temperature, which is input to the program and used to accept or reject moves, with a configurational temperature kBTconfig=|∇qΦ|2/∇q2Φ. Here, Φ is the potential energy of the system and ∇q represents the dimensionless gradient operator with respect to the particle positions q. We show, using a simulation of Lennard-Jones particles, that the configurational temperature rapidly and accurately tracks changes made to the input temperature even when the system is not in global thermodynamic equilibrium. Coding and/or algorithm errors can be detected by checking that the input temperature and Tconfig agree. The effects of system size and continuity of Φ and its first derivative on Tconfig are also discussed.