THERMODYNAMIC FUNCTION, FRACTAL DIMENSION AND CRITICAL SLOWING-DOWN

The paper shows how the characteristic time exponent z in slowing down , and the fractal dimension of the order parameter field, are uniquely determined by distinct forms of special thermodynamic functions that describe the interacting systems with some terms of phi(n). It is also shown that for the purpose of obtaining critical exponents, the renor malization group transformation is needed just to perform to the power s of the order parameter and not to their coefficients in thermodynami c functions. This advantage leads to results which are analytically ex act.