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We point out that ignoring nonlinear effects in finite size scaling may leadto errors in estimates of the critical temperature and Binder cumulants. Weshow that the order of magnitude of these effects can be estimated from data atrelatively small volume. Using this estimate, we propose to use linear fits inincreasingly small temperature regions as the volume is increased (rather thanusing a fixed temperature interval). The choice of the exact coefficient ofproportionality can be optimized and reveals interesting crossing patternsamong estimates. We show that the new procedure works very well for Dyson'shierarchical model. We discuss applications of the method for 3 dimensionalspin models and finite temperature lattice gauge theories and comment on thenonlinear effects for existing calculations.

How to control nonlinear effects in Binder cumulants