The critical behaviour of the 1-dimensional XY model with power law decay long range interactions

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We discuss the critical behaviour of the 1-dimensional classical XY model with power law decay long range interactions by using Monte Carlo simulation. It has been predicted by renormalization group calculation that the critical behaviour changes with the power of interactions. From the simulation result of temperature dependence of the specific heat, we confirm that the system shows the critical behaviour of the mean field type and the non-trivial long range order. We also estimate the critical exponent η for the system with the inverse square long range interactions, and by using the phenomenological renormalization group plot, we confirm the 'Berezinskii-Kosterlitz-Thouless (BKT)-like' transition which has been predicted by the spin wave calculations.