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A Hamiltonian dynamics is defined for the XY model by adding a kinetic energyterm. Thermodynamical properties (total energy, magnetization, vorticity)derived from microcanonical simulations of this model are found to be inagreement with canonical Monte-Carlo results in the explored temperatureregion. The behavior of the magnetization and the energy as functions of thetemperature are thoroughly investigated, taking into account finite sizeeffects. By representing the spin field as a superposition of random phasedwaves, we derive a nonlinear dispersion relation whose solutions allow thecomputation of thermodynamical quantities, which agree quantitatively withthose obtained in numerical experiments, up to temperatures close to thetransition. At low temperatures the propagation of phonons is the dominantphenomenon, while above the phase transition the system splits into ordereddomains separated by interfaces populated by topological defects. In the hightemperature phase, spins rotate, and an analogy with an Ising-like system canbe established, leading to a theoretical prediction of the critical temperature$T_{KT}\approx 0.855$.Comment: 10 figures, Revte

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Hamiltonian dynamics and the phase transition of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>model

Hamiltonian dynamics and the phase transition of theXYmodel