A powerful computational method for dealing with correlation functions in magnetic systems, based on damage-spreading simulations, is reviewed and tested, by investigating the $q$-state Potts ferromagnet, on a square lattice, at criticality. Exact relations involving special kinds of damage and the spin-spin correlation function, as well as the magnetization, are used. The efficiency of the method arises with a significant reduction of the finite-size effects, with respect to conventional Monte Carlo simulations. Correlation functions, which represent usually a hard task within this latter procedure, appear to be much more easily estimated through the present damage-spreading simulations. The effectiveness of the technique is illustrated by an accurate estimate of the exponent $\eta$, of the spin-spin correlation function, for $q=2$, 3, and 4, with rather small lattice sizes. In the cases $q⩾5$, an analysis of the magnetization is consistent with the well-known first-order phase transition.

• Received 23 March 2006

DOI:https://doi.org/10.1103/PhysRevE.74.016703