CASIMIR EFFECT IN CRITICAL SYSTEMS - A MONTE-CARLO SIMULATION

If a critical system is confined to a finite geometry, critical fluctu ations 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 Casimi r amplitudes directly and accurately. We apply the algorithm to a crit ical q-state Potts model confined to a rectangular M X L geometry in d =2 dimensions and to a critical Ising model confined to a M(2) X L geo metry in d=3 dimensions. We find good agreement with rigorous results in d=2 and compare our results with field-theoretic estimates of the C asimir amplitude in d=3.