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We apply the self-consistent harmonic approximation (SCHA) to study staticand dynamic properties of the two-dimensional classical Heisenberg model witheasy-axis anisotropy. The static properties obtained are magnetization and spinwave energy as functions of temperature, and the critical temperature as afunction of the easy-axis anisotropy. We also calculate the dynamic correlationfunctions using the SCHA renormalized spin wave energy. Our analytical results,for both static properties and dynamic correlation functions, are compared tonumerical simulation data combining cluster-Monte Carlo algorithms and SpinDynamics. The comparison allows us to conclude that far below the transitiontemperature, where the SCHA is valid, spin waves are responsible for allrelevant features observed in the numerical simulation data; topologicalexcitations do not seem to contribute appreciably. For temperatures closer tothe transition temperature, there are differences between the dynamiccorrelation functions from SCHA theory and Spin Dynamics; these may be due tothe presence of domain walls and solitons.Comment: 12 pages, 14 figure

Low-temperature static and dynamic behavior of the two-dimensional easy-axis Heisenberg model