Erdem, R.Yalcin, O.2024-11-072024-11-072018978-981-3224-97-1978-981-3224-96-4https://hdl.handle.net/11480/1376414th Regional Conference on Mathematical Physics -- NOV 09-14, 2015 -- Quaid i Azam Univ, Islamabad, PAKISTANExact free energy values of the spin-1 mean-field Ising model for finite systems that consist of N particles have been calculated in the microcanonical formalism which uses the gamma function. We have constructed the contour maps of the free energy surfaces in the phase space of dipolar (M) and quadrupolar (Q) order parameters for various values of N. From these maps, stable, metastable and unstable states are seen explicitly. We have analyzed these states in comparison with the free energy values obtained by using the approximated expression for the entropy using the Stirling approximation to deal with factorials. Moreover, the relative error between our exact values and the approximate one using the Stirling formula has been calculated and displayed as the contour map in the M - Q phase space.eninfo:eu-repo/semantics/closedAccessSpin-1 Mean-Field Ising ModelFree Energy SurfacesContour MappingGamma FunctionConference Object311319WOS:000459731000033N/A