New scaling relations in classical spin models with long-range order

A clear evidence is presented that the classical spin models with long-range order are characterized by the phase coherence of universal nature. A block transformation technique is used to introduce a new type of order parameter relevant to the phase coherence of the whole state. The phase coherence in the classical spin models was studied in detail by means of Monte Carlo simulations. The results obtained are: (1) the phase coherence and its fluctuation exhibit a universal behavior above the transition temperature and can be expressed in terms of a simple scaling function; and (2) the specific form of the scaling function leads to two new scaling relations which hold well in all the spin models studied.