Vortex- antivortex pairs

For an XT-model at dimensionalities d > dt this coefficient vanishes at Tc with a power law S a ]f 2jff T,v. Although in d = 2 the magnetization (cos0(x)) = 0, the stiffness S is non-zero in the spin wave regime in fact, comparison of eqs. (160) and (168) suggests S = J, independent of T. The Kosterlitz-Thouless (1973) theory implies that S is reduced from J at non-zero temperatures due to vortex-antivortex pairs, and that the equation that yields the transition temperature rather is... 

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