Long-range interaction Blume-Emery-Griffiths model:Critical exponents in microcanonical ensemble

We investigate the thermodynamic quantities of Blume-Emery-Griffiths model with long-range interactions and observe negative specific heat and susceptibility near the first order line,where the temperature,specific heat and susceptibility are discontinuity.When order-disorder phase transition takes place,the critical exponent of specific heat(a=a'=0) and the critical exponent of susceptibility(γ=γ'=1) are consistent with the prediction of mean field theory.However,when coupling constant corresponds to the value of canonical tri-critical point,the critical exponent of specific heat and susceptibility take the values of 0=a≠a'=1 and 1=γ≠γ'=2.The critical exponents violate the scaling homogeneity equalities and a'+β+γ'2 breaks down the Widom scaling law.