Casimir effect in critical systems: A Monte Carlo simulation

If a critical system is confined to a finite geometry, critical fluctuations of the order parameter generate long-ranged forces between the system boundaries. These forces, commonly known as Casimir forces, are characterized by universal amplitudes and scaling functions. A hybrid Monte Carlo algorithm has been devised and used to measure the Casimir amplitudes directly and accurately. We apply the algorithm to a critical q-state Potts model confined to a rectangular M×L geometry in $d=2$ dimensions and to a critical Ising model confined to a M²×L geometry in $d=3$ dimensions. We find good agreement with rigorous results in $d=2$ and compare our results with field-theoretic estimates of the Casimir amplitude in $d=3$.