An efficient algorithm simulating a macroscopic system at the critical point

.A.Tsolias Itiswellknown thatconventionalsim ulation algorithm sare ine(cid:14) cientforthe statisticaldescrip-tion ofm acroscopic system sexactly atthecriticalpointdue to the divergence ofthe corresponding relaxation tim e (criticalslowing down). O n the other hand the dynam ics in the order param eter space issim pli(cid:12) ed signi(cid:12) cantly in thiscase due to the onsetofself-sim ilarity in the associated (cid:13) uc-tuation patterns. A s a consequence the e(cid:11) ective action at the criticalpoint obtains a very sim ple form . In the present work we show that this sim pli(cid:12) ed action can be used in order to sim ulate e(cid:14) ciently the statisticalpropertiesofa m acroscopic system exactly atthe criticalpoint.U sing the proposed algorithm we generate an ensem ble ofcon(cid:12) gurationsresem bling the characteristic fractal geom etry ofthe criticalsystem related to the self-sim ilar order param eter (cid:13) uctuations. A s an ex-am ple we sim ulate the one-com ponent realscalar (cid:12) eld theory at the transition point T = T c as a representative system belonging to the 3 (cid:0) D Ising universality class.