the coherent anomaly method in the studying of the s=1 ising chains with long-range interaction

the coherent anomaly method and a cluster mean-field approach combined with finite-sizescaling extrapolation were used to determine the critical temperature and the critical exponents of as =1 ising chain with a long-range interaction in the form of 1/ r1+σ . the results of criticaltemperature are in good agreement with the recent results of the finite-range scaling method and aremore accurate in the classical region. the critical exponents are in agreement with the results of spin-21ising chains and indicate that the critical exponents are independent of the magnitude of spin in isingmodels with long-range interactions.