FINITE-SIZE-SCALING AT 1ST-ORDER PHASE-TRANSITIONS

It is demonstrated that finite size scaling at first order phase transitions is something basically very simple: As the number of particles N in the system goes to infinity, s(N)(epsilon), the entropy per particle, rapidly approaches its limiting behaviour s(infinity)(epsilon). Once s(infinity) (epsilon) has been determined, the thermal behaviour of the infinite system is completely known and in case of a first order phase transition the specific heat exhibits a delta-function singularity. If, however, the specific heat c(N)(T) per particle is calculated from the canonical partition function Z(N)(beta) = integral d epsilon exp {N[s(N)(epsilon) - betaepsilon]}, then even if s(N)(epsilon) is replaced by its limiting form s(infinity)(epsilon), c(N)(T) only exhibits a peak with a finite maximum value proportional to N which is due to the explicit factor N in front of the angular bracket in the exponent. This is the N-dependence which has recently been called finite size scaling at first order phase transitions. The entropy S(N)(epsilon) can very efficiently be determined in the dynamical ensemble.